Pith. sign in

REVIEW 3 major objections 4 minor 4 cited by

(-1)-form symmetries from M-theory and SymTFTs

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that (-1)-form symmetries of M-theory-engineered QFTs are determined by the link's cohomology: finite ones by $\mathrm{Tor}H^4(L_{10-d},\mathbb{Z})$ and continuous ones by $H^3(L_{10-d},\mathbb{Z})_{\mathrm{free}}$, with…

desk verdict A substantial, mostly well-cross-checked extension of the SymTFT program to (-1)-form symmetries, whose load-bearing differential-cohomology prescription is admitted to be a proposal and deserves referee scrutiny. read the letter →

arxiv 2411.19683 v3 pith:K2EXCYK6 submitted 2024-11-29 hep-th

Marwan Najjar , Leonardo Santilli , Yi-Nan Wang This is my paper · ORCID
classification hep-th
keywords (-1)-formsymmetriesSymmetryTopologicalFieldTheoryM-theorygeometricengineeringdifferentialcohomologyhigher-formG2holonomy4-groupBFterms
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's central claim is that $(-1)$-form symmetries of quantum field theories built by M-theory geometric engineering are not accidental: they are read directly from the cohomology of the link $L_{10-d}$ of the internal cone. Finite $(-1)$-form symmetries appear when $\mathrm{Tor}H^4(L_{10-d},\mathbb{Z})$ is non-trivial, and continuous ones when $H^3(L_{10-d},\mathbb{Z})_{\mathrm{free}}$ is non-trivial, with the corresponding background fields obtained by expanding the differential-cohomology refinement of the M-theory 4-form $G_4$. The paper also proposes that refining the kinetic term $G_4 \wedge G_7$ to the Cheeger--Simons character $\breve{G}_4 \star \breve{dG}_7$ and reducing over the link yields, in one stroke, all BF couplings of the SymTFT for both discrete and continuous symmetries, while the anomalous twist terms come from $\int C_3 \wedge G_4 \wedge G_4$. If this is right, the whole $(-1)$-form symmetry sector, including mixed anomalies and polarization choices, becomes a purely topological computation for 5d and 4d supersymmetric theories, and the G2 example shows how it connects to 4-group structures and modified instanton sums.

What carries the argument

The central object is the differential character $\breve{G}_4 \star \breve{dG}_7$, the conjectural Cheeger--Simons uplift of the M-theory kinetic term $G_4 \wedge G_7$; reducing it fibrewise over the link $L_{10-d}$ generates the BF terms of the SymTFT. The matching symmetry operators are brane holonomies: M5-branes on torsional cycles for finite $(-1)$-form symmetries, and $P_7$-fluxbranes on free cycles for continuous ones, where $P_7 = G_7 + \frac{1}{4\pi} H_3 \wedge G_4$ is the Page charge whose closedness and quantization make the operators topological. The mechanism works because the holonomy pairing (2.20) projects out exactly the discrete gauge fields, while the completion of the free-cycle BF term by the Chern--Simons twist term turns the non-closed $h$ into a closed quantized $\hat{h}$.

What would settle it

Take a 4d $\mathcal{N}=1$ SU(N) Yang--Mills theory and gauge only a $\mathbb{Z}_p$ subgroup of the 2-form symmetry on a four-manifold with $b_2 > 0$: the paper predicts that instanton numbers must be multiples of $p$ and that $\theta_{\mathrm{YM}}$ has period $2\pi/p$, so a direct instanton or partition-function computation that finds no such restriction would falsify the 4-group claim.

Watch

Extended reading notes

Core claim

The paper establishes a geometric dictionary for $(-1)$-form symmetries in M-theory: finite ones are engineered by M5-branes filling spacetime and wrapping torsional $(6-d)$-cycles of the link, while continuous ones are engineered by spacetime-filling $P_7$-fluxbranes wrapping free $(7-d)$-cycles. The load-bearing identity is the differential-cohomology refinement of the M-theory kinetic term, $\breve{G}_4 \star \breve{dG}_7$, whose fibrewise integral over the link produces the BF terms: torsion--torsion reductions give $B_{p+1} \smile \delta A_{d-p-1}$ for finite electric/magnetic pairs, and free--free reductions give $F_{p+2} \wedge h_{d-p-1}$, corrected by a contribution from $\int C_3 \wedge G_4 \wedge G_4$ into a closed, quantized field $\hat{h}_{d-p-1}$. Applied to 5d SCFTs from Calabi--Yau threefold singularities, this shows that every torsional $H^2(L_5,\mathbb{Z})$ class generates a dual $(-1)$-form/4-form pair with a polarization choice that had been overlooked. For the 4d $\mathcal{N}=1$ theory from M-theory on the G2 quotient $B_7/\Gamma_{p,N,q}$, the paper claims a discrete $\mathbb{Z}_p$ $(-1)$-form symmetry, two continuous $(-1)$-form symmetries, and the identification $\hat{h}^f_4/(2\pi) \leftrightarrow \mathrm{tr}\{F \wedge F\}/(8\pi^2)$ with the Chern--Weil symmetry shifting $\theta_{\mathrm{YM}}$; gauging the electric 1-form, 3-form, and a $\mathbb{Z}_p$ subgroup of the 2-form symmetry simultaneously yields the 4-group $(\mathbb{Z}_N^{[1]} \times \mathbb{Z}_p^{[2]}) \rtimes \mathbb{Z}_p^{[3]}$ and modified instanton sums.

Load-bearing premise

The derivation rests on a single proposed rule: that the M-theory kinetic term is correctly lifted to the differential character $\breve{G}_4 \star \breve{dG}_7$, together with the completion rule that combines the resulting BF term with a Chern--Simons correction; the paper explicitly says it lacks a more comprehensive explanation for this procedure and that it matches the expected results only in the cases considered.

Editorial extensions

If this is right

  • Any M-theory-engineered QFT whose link has $\mathrm{Tor}H^4(L_{10-d},\mathbb{Z}) \neq 0$ carries a finite $(-1)$-form symmetry, and the BF coefficient fixes the discrete $\theta$-angle of the dual symmetry.
  • In 5d SCFTs, every torsional $H^2(L_5,\mathbb{Z})$ class automatically yields a $(-1)$-form/4-form dual pair, so specifying the global form of the theory requires a polarization choice for this pair as well.
  • In the 4d $\mathcal{N}=1$ G2 model, one of the two continuous $(-1)$-form symmetries is the expected Chern--Weil symmetry shifting $\theta_{\mathrm{YM}}$, while the other is a new symmetry from the higher-dimensional origin, changing the anomaly structure of the low-energy theory.
  • Gauging $\mathbb{Z}_N^{[1]}$, $\mathbb{Z}_p^{[3]}$, and $\mathbb{Z}_p^{[2]}$ together gives the 4-group structure $(\mathbb{Z}_N^{[1]} \times \mathbb{Z}_p^{[2]}) \rtimes \mathbb{Z}_p^{[3]}$, reproducing the field-theoretic results of modified instanton sums from pure geometry.
  • If only $\mathbb{Z}_p \subset U(1)^{[2]}$ is gauged, the instanton number of the SU(N) gauge theory is forced to be a multiple of $p$ and $\theta_{\mathrm{YM}}$ becomes $2\pi/p$-periodic.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The link-cohomology criterion would give a purely topological search tool: any conical Calabi--Yau or G2 space with torsion in $H^4$ of its link would predict a $(-1)$-form symmetry before any field-theory computation, opening a systematic scan of the geometric landscape.
  • The $P_7$-fluxbrane construction suggests an analogous prescription for Type II string theory compactifications, where the relevant Page charge and Chern--Simons corrections differ; verifying the completion rule there would test the general principle beyond the M-theory examples.
  • The least constrained step is the completion rule that turns the BF term into a closed quantized field; a first-principles derivation of eq. (2.13) would convert the empirically matched procedure into a theorem, and would likely fix the coefficients in cases with more than two nontrivial symmetries.
  • The 4-group prediction is directly testable in 4d gauge theory: computing the SU(N) partition function with a gauged $\mathbb{Z}_p$ 2-form subgroup on a manifold with $b_2 > 0$ should show $\theta_{\mathrm{YM}}$ periodicity $2\pi/p$ and instanton numbers divisible by $p$.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper develops a formalism for computing (-1)-form symmetries and their SymTFTs from M-theory geometric engineering. The central proposal is to refine the M-theory kinetic term G4 ∧ G7 to the differential character ˘G4 ⋆ ˘dG7 (Eq. (2.13)) and to complete the resulting BF-like terms F ∧ h into couplings F ∧ ĥ with ĥ closed and quantized via a contribution from the Chern-Simons term (Eqs. (2.41)-(2.43)). From this, the paper derives SymTFT actions for 5d N=1 SCFTs, 4d N=2 KK theories, and 4d N=1 theories on G2-manifolds of the type B7/Γ_{p,N,q}. It identifies discrete Z_p and continuous U(1) (-1)-form symmetries, matches known anomaly coefficients such as (N-1)/N, and reproduces the 4-group structure and modified instanton sum of [116]. The paper also constructs symmetry operators from P7-fluxbranes, refining earlier proposals for continuous abelian symmetries.

Significance. If the proposed refinement and completion rules are correct, the paper provides a genuinely systematic top-down method: the (-1)-form symmetry sector of an M-theory-engineered QFT would be computable from the cohomology of the link L_{10-d}, with BF terms and mixed anomalies obtained from a single differential-cohomology action. The paper's strengths are its concreteness and cross-checks: the geometric integrals are explicit, the lens-space coefficients match [49, 57], the local P1×P1 triple intersections match [31], and anomaly coefficients reproduce field-theory results [81, 116, 140]. The fluxbrane construction of continuous symmetry operators is also a useful clarification. However, the central derivation is contingent on an unproven uplift and an openly admitted completion rule, so the significance of the main claim depends on resolving that ambiguity.

major comments (3)
  1. [Section 2.1.2, Eq. (2.13)] The entire BF-term derivation rests on the proposal that the M-theory kinetic term refines to the differential character holonomy ∫_{M11} ˘G4 ⋆ ˘dG7. This is not derived from a first principle: the modified Bianchi identity dG7 = -G4∧G4/(2(2π)) does not by itself select this particular differential cohomology uplift, and ˘dG7 is not the differential character of G7. Since every subsequent SymTFT action (Eqs. (3.16), (3.37), (4.12), (4.40)) inherits this premise, a different but a priori consistent refinement would change the claimed BF coefficients. The authors should either give a systematic derivation of (2.13) or present it explicitly as a conjecture with a clear testable criterion.
  2. [Section 2.2.3, Eqs. (2.41)-(2.43)] The completion of the BF-like term F ∧ h into F ∧ ĥ with closed quantized ĥ is implemented by adding a contribution from the Chern-Simons reduction with coefficients fixed to match the known symmetry operators. The text states: "While we lack a more comprehensive explanation, this procedure is suited to match the combined BF terms and the symmetry topological operators in all cases considered in the present work." This is a load-bearing point rather than a presentation matter, because the same completion rule is used both to produce the SymTFT actions in Sections 3 and 4 and to identify the field-theoretic anomaly coefficients and the 4-group structure in Section 4.4. As written, the derivation is close to circular: the rule is tuned on the same data it is then used to predict. I request a more principled criterion for when the twist-term correction must be added and an independent check in at least one example where the coefficient is not already an input.
  3. [Section 4.4, Eqs. (4.73)-(4.86)] The derivation of the 4-group structure and the modified instanton sum depends on several choices that are not derived from the geometry: the selection K=p for the gauged subgroup of U(1)[2], the non-trivial transformation of a4 in Eq. (4.74), and the relaxation of the discreteness condition for a4 in Eq. (4.80). These choices are motivated by agreement with [116], but the paper does not explain whether they are forced by the link geometry L6=(S3_f/Z_{pN})×(S3_b/Z_p) or by the field-theoretic outcome one wants to reproduce. Without such a derivation, the geometric-engineering claim for the 4-group structure is weaker than the summary suggests. Please clarify which of these choices are uniquely fixed by the M-theory data and which are additional input.
minor comments (4)
  1. [Throughout] The spelling "Chern-Weyl" is used in several places (e.g., Sections 1.1 and 4.1.2) where the standard name is "Chern-Weil"; please unify.
  2. [Eq. (2.44)] The quantity eH_{d-2+k} is introduced as the curvature of a sum but its field-strength map and normalization are not defined before use; please define it explicitly.
  3. [Appendix B.2.2, Eq. (B.17)] The boundary projection operator eδ is described in footnote 12 as a book-keeping device without a precise definition. Since it carries substantial weight in the projection of the SymTFT to the physical boundary, a more formal characterization or a citation to a rigorous construction would improve clarity.
  4. [Section 4.3.1, Eq. (4.41)] In the p=1 special case, the notation B7/Γ_{p,N,q} with the assumptions gcd(p,N)=1 and N>p needs a brief comment on how N is chosen; otherwise the reader may wonder whether p=1 is compatible with the constraints.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: central coefficients are fixed by link topology and benchmarked against independent field-theory results.

full rationale

The paper's derivation chain is not circular. The symmetry content is read off from the cohomology of the link via a standard Kaluza-Klein expansion of the differential character ˘G4 (eqs. 3.7, 4.31), and the BF coefficients in eqs. 3.16, 3.37 and 4.40 are explicit integrals over torsion classes computed in Appendix A.3, not fitted parameters. The anomaly coefficients in (4.35) come from triple intersections over lens spaces and agree with independent field-theoretic results, notably the 1/N coefficient in the θYM anomaly (4.42)-(4.44), the 4-group structure (4.83) and the modified instanton sum (4.86) of [116]. The one admitted non-derivation is the differential-cohomology uplift (2.13) and the completion rule (2.43); Section 2.2.3 states, 'While we lack a more comprehensive explanation, this procedure is suited to match the combined BF terms and the symmetry topological operators in all cases considered in the present work.' This is an acknowledged assumption, not a circular step: the completion rule is not fitted to the predicted anomalies but is fixed by reducing the M-theory Chern-Simons term (2.10), and it is checked against the independently defined P7-fluxbrane operator (2.33). The G2 geometry is imported from [22], authored by one of the present authors, but it is a published, externally falsifiable geometric construction used as input rather than as evidence for the SymTFT claims. No equation in the paper reduces to its own input by construction.

Assumptions & free parameters 3 free parameters · 8 assumptions · 2 invented entities

No continuous free constants are fitted to data; the anomaly coefficients are computed from topology (intersection numbers, linking pairings) and agree with independent field-theory results, which is the strongest evidence of non-circularity. The load-bearing input that the reader did not pay for upstream is concentrated in two ad-hoc proposals: the differential uplift (2.13) and the P7 Page-charge fluxbrane (2.33), plus two domain assumptions from the authors' own prior work: the SymTFT-from-M-theory dictionary [49] and the G2 engineering of su(N) SYM [22]. The gauging choices of Section 4.4 act as discrete free parameters tuned to reproduce [116].

free parameters (3)
  • Gauging choices in the 4-group derivation = K = p; θ(2) = -θ(3); χ(1) = χ(3); pa4 = da3 + (N/4π) b2∧b2
    Chosen in Section 4.4 to reproduce the 4-group structure and modified instanton sum of [116, 117]; the alternative solution χ(1)=0 is discarded. These are discrete choices, not continuous fits, but they are selected with the target result in view.
  • Torsion generator conventions = holonomy exp(2πi(n-1)/n) for lens-space generator; κ(5) = -1/mα δαα′
    Appendix A.3.2 notes that the holonomy value 'depends on the choice of u1, each choice corresponding to a different generator'; conventions are fixed to match [49] rather than determined by geometry alone. These choices affect signs and coefficients in the SymTFT.
  • Normalization of free-cycle pairing integrals = ∫_L PD(γk) ∧ vk := 1
    Sections 2.2.2-2.2.3 set non-vanishing link integrals to 1 'without loss of generality'; this rescaling fixes the normalization of the symmetry operator phases.
assumptions (8)
  • standard math Cheeger-Simons differential cohomology: integration map, ⋆-product, holonomy of torsion characters, external products
    The formal backbone of the BF-term and anomaly computations (Sections 2.1.1, 2.1.2; Appendix A.2).
  • domain assumption M-theory low-energy action with G4, G7, modified Bianchi identity dG7 = -(1/(4π)) G4∧G4, and Chern-Simons term (2.10)
    Standard 11d supergravity in democratic formalism; conventions in Section 2.1.2 and Appendix C.
  • domain assumption Geometric engineering dictionary: QFT = M-theory on a cone over link L; SymTFT from reduction along L with the radial direction as the SymTFT interval
    The framework (eqs. 1.1-1.4) established in [49] and the geometric engineering literature; the paper extends it to (-1)-form symmetries.
  • ad hoc to paper The kinetic term admits the differential uplift ˘G4 ⋆ ˘dG7 (eq. 2.13), and the resulting BF terms combine with twist-term corrections into a closed quantized field
    Proposed in this paper; Section 2.2.3 admits the combination rule lacks a general derivation and is matched example by example.
  • ad hoc to paper P7 (Page charge, eqs. 2.30-2.31) is closed and 2π-quantized, and P7-fluxbranes generate the U(1) symmetry operators (2.33)
    Proposed construction in Section 2.2.2 using the Hopf-Wess-Zumino action on M5-branes; closure uses the modified Bianchi identity and the worldvolume relation dH3 = ι*G4.
  • domain assumption The B7 family of G2-holonomy metrics exists, and the abelian quotient Γ_{p,N,q} with gcd conditions (4.18) preserves G2 holonomy and acts as in (4.19)
    From [107, 145, 22]; the link topology (S³/Z_{pN}) × (S³/Z_p) for q≠0 stated in (4.23) is the geometric input for all Section 4.3 results.
  • domain assumption On the semi-classical branch, M-theory on B7/Γ_{p,N,q} engineers 4d N=1 su(N) SYM with Z_p acting freely, so the effective electric 1-form symmetry is Z_N, not Z_{pN}
    Inherited from [22]; Section 4.3.2 uses it to identify the Chern-Weil symmetry, the 2π/p theta periodicity, and to set up the 4-group gauging in Section 4.4.
  • ad hoc to paper The boundary projection operator δ maps SymTFT fields to the physical boundary and handles gauged top-form fields (eqs. B.17-B.22)
    Defined in Appendix B.2.2; footnote 12 calls it 'a book-keeping device' and declines a rigorous definition; Section 4.4's 4-group and instanton-sum derivation depends on it.
invented entities (2)
  • P7-fluxbrane
    purpose: Non-BPS fluxbrane carrying the Page charge P7 on a seven-dimensional worldvolume; generates continuous U(1) symmetry operators, replacing the non-topological naive G7-fluxbrane
    Proposed in Section 2.2.2; topological invariance follows from the equations of motion and the HWZ action, providing internal consistency but no external falsifiable handle beyond the framework itself.
  • Second continuous (-1)-form symmetry U(1)^{[-1,b]} in the G2 model
    purpose: A new Chern-Weil-type symmetry beyond the theta shift, traced to the S³_b/Z_p factor of the link; contributes to the 4-group structure
    Uncovered in Section 4.3; its support is the internal SymTFT computation plus agreement with the field-theory construction [116], whose structure the paper sets out to reproduce.

how reviews work

0 comments
Cite this review

Pith. "Pith review of (-1)-form symmetries from M-theory and SymTFTs." pith.science (2026). https://pith.science/paper/K2EXCYK6

@misc{pith2026241119683,
  author       = {Pith},
  title        = {Pith review of: (-1)-form symmetries from M-theory and SymTFTs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K2EXCYK6}},
  note         = {Machine review of arXiv:2411.19683}
}
abstract

We explore $(-1)$-form symmetries within the framework of geometric engineering in M-theory. By constructing the Symmetry Topological Field Theory (SymTFT) for selected 5d $\mathcal{N}=1$, 4d $\mathcal{N}=2$ and 4d $\mathcal{N}=1$ theories, we formalize the geometric origin of these symmetries and compute the mixed anomaly polynomials involving $(-1)$-form and higher-form symmetries. Our findings consistently reveal both discrete and continuous $(-1)$-form symmetries, aligning with established field theory results, while also uncovering new $(-1)$-form symmetry factors and structural insights. In particular, we study the SymTFT of 4d $\mathcal{N}=1$ theories from M-theory on a class of spaces with $G_2$ holonomy, and obtain properties such as modified instanton sums and 4-group structures observed in other 4d gauge theories. Additionally, we systematically construct symmetry operators for continuous abelian symmetries, refining existing proposals, and providing an M-theory origin for them.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Generalized Families of QFTs

    hep-th 2026-02 unverdicted novelty 7.0 of 10

    Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.

  2. SymTFTs and Non-Invertible Symmetries of 6d (2,0) SCFTs of Type $D$ from M-theory

    hep-th 2024-12 conditional novelty 7.0 of 10

    The 7d SymTFT for 6d (2,0) D_N SCFTs is derived from M-theory on AdS7 × RP4, including the outer-automorphism Z2 sector, and is used to derive non-invertible symmetries and anomaly polynomials.

  3. Notes on (-2)-form symmetries

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...

  4. SymTFT actions, Condensable algebras and Categorical anomaly resolutions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.

Reference graph

Works this paper leans on

173 extracted references · 16 canonical work pages · cited by 4 Pith papers

  1. [116]

    Tanizaki and M

    Y. Tanizaki and M. ¨Unsal, Modified instanton sum in QCD and higher-groups , JHEP 03 (2020) 123, [ 1912.01033]

    arXiv 2020

  2. [22]

    B. S. Acharya, L. Foscolo, M. Najjar and E. E. Svanes, New G 2-conifolds in M-theory and their field theory interpretation , JHEP 05 (2021) 250, [ 2011.06998]

    arXiv 2021

  3. [31]

    Closset, M

    C. Closset, M. Del Zotto and V. Saxena, Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective, SciPost Phys. 6 (2019) 052, [ 1812.10451]

    arXiv 2019

  4. [2]

    C. G. Callan, Jr. and J. A. Harvey, Anomalies and Fermion Zero Modes on Strings and Domain Walls , Nucl. Phys. B 250 (1985) 427–436

    1985

  5. [1]

    ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking , NATO Sci

    G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking , NATO Sci. Ser. B 59 (1980) 135–157

    1980

  6. [3]

    Aharony, N

    O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, JHEP 08 (2013) 115, [ 1305.0318]

    arXiv 2013

  7. [4]

    Gaiotto, A

    D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized Global Symmetries, JHEP 02 (2015) 172, [ 1412.5148]

    arXiv 2015

  8. [5]

    K. G. Wilson, Confinement of Quarks , Phys. Rev. D 10 (1974) 2445–2459

    1974

Show all 173 references
  1. [6]

    ’t Hooft, On the Phase Transition Towards Permanent Quark Confinement , Nucl

    G. ’t Hooft, On the Phase Transition Towards Permanent Quark Confinement , Nucl. Phys. B 138 (1978) 1–25

    1978

  2. [7]

    S. H. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories , Nucl. Phys. B 497 (1997) 173–195, [ hep-th/9609239]

    1997 arXiv

  3. [8]

    Atiyah, J

    M. Atiyah, J. M. Maldacena and C. Vafa, An M theory flop as a large N duality , J. Math. Phys. 42 (2001) 3209–3220, [ hep-th/0011256]

    2001 arXiv

  4. [9]

    B. S. Acharya, On Realizing N=1 superYang-Mills in M theory , hep-th/0011089

    arXiv

  5. [10]

    B. S. Acharya and C. Vafa, On domain walls of N=1 supersymmetric Yang-Mills in four-dimensions, hep-th/0103011

    arXiv

  6. [11]

    Atiyah and E

    M. Atiyah and E. Witten, M theory dynamics on a manifold of G(2) holonomy , Adv. Theor. Math. Phys. 6 (2003) 1–106, [ hep-th/0107177]

    2003 arXiv

  7. [12]

    B. S. Acharya, Confining strings from G(2) holonomy space-times , hep-th/0101206

    arXiv

  8. [13]

    Beasley and E

    C. Beasley and E. Witten, A Note on fluxes and superpotentials in M theory compactifications on manifolds of G(2) holonomy , JHEP 07 (2002) 046, [ hep-th/0203061]

    2002 arXiv

  9. [14]

    Berglund and A

    P. Berglund and A. Brandhuber, Matter from G(2) manifolds , Nucl. Phys. B 641 (2002) 351–375, [hep-th/0205184]

    2002 arXiv

  10. [15]

    B. S. Acharya and S. Gukov, M theory and singularities of exceptional holonomy manifolds , Phys. Rept. 392 (2004) 121–189, [ hep-th/0409191]

    2004 arXiv

  11. [16]

    L. B. Anderson, A. B. Barrett, A. Lukas and M. Yamaguchi, Four-dimensional Effective M-theory on a Singular G(2) Manifold , Phys. Rev. D 74 (2006) 086008, [ hep-th/0606285]. – 89 –

    2006 arXiv

  12. [17]

    Halverson and D

    J. Halverson and D. R. Morrison, The landscape of M-theory compactifications on seven-manifolds with G 2 holonomy, JHEP 04 (2015) 047, [ 1412.4123]

    2015 arXiv

  13. [18]

    Halverson and D

    J. Halverson and D. R. Morrison, On gauge enhancement and singular limits in G 2 compactifications of M-theory, JHEP 04 (2016) 100, [ 1507.05965]

    2016 arXiv

  14. [19]

    A. P. Braun, M. Del Zotto, J. Halverson, M. Larfors, D. R. Morrison and S. Sch¨ afer-Nameki,Infinitely many M2-instanton corrections to M-theory on G 2-manifolds, JHEP 09 (2018) 077, [ 1803.02343]

    2018 arXiv

  15. [20]

    Kennon, G2-Manifolds and M-Theory Compactifications , 1810.12659

    A. Kennon, G2-Manifolds and M-Theory Compactifications , 1810.12659

    arXiv

  16. [21]

    A. P. Braun, S. Cizel, M. H¨ ubner and S. Sch¨ afer-Nameki,Higgs bundles for M-theory on G2-manifolds, JHEP 03 (2019) 199, [ 1812.06072]

    2019 arXiv

  17. [23]

    Del Zotto, J

    M. Del Zotto, J. Oh and Y. Zhou, Evidence for an algebra of G 2 instantons, JHEP 08 (2022) 214, [ 2109.01110]

    2022 arXiv

  18. [24]

    A. P. Braun, E. Sabag, M. Sacchi and S. Schafer-Nameki, G2-Manifolds from 4d N=1 Theories, Part I: Domain Walls , SciPost Phys. 17 (2024) 102, [ 2304.01193]

    2024 arXiv

  19. [25]

    K. A. Intriligator, D. R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces , Nucl. Phys. B497 (1997) 56–100, [hep-th/9702198]

    1997 arXiv

  20. [26]

    Esole, S.-H

    M. Esole, S.-H. Shao and S.-T. Yau, Singularities and Gauge Theory Phases , Adv. Theor. Math. Phys. 19 (2015) 1183–1247, [ 1402.6331]

    2015 arXiv

  21. [27]

    Esole, S.-H

    M. Esole, S.-H. Shao and S.-T. Yau, Singularities and Gauge Theory Phases II , Adv. Theor. Math. Phys. 20 (2016) 683–749, [ 1407.1867]

    2016 arXiv

  22. [28]

    Del Zotto, J

    M. Del Zotto, J. J. Heckman and D. R. Morrison, 6D SCFTs and Phases of 5D Theories , JHEP 09 (2017) 147, [ 1703.02981]

    2017 arXiv

  23. [29]

    Xie and S.-T

    D. Xie and S.-T. Yau, Three dimensional canonical singularity and five dimensional N = 1 SCFT, JHEP 06 (2017) 134, [ 1704.00799]

    2017 arXiv

  24. [30]

    Esole, M

    M. Esole, M. J. Kang and S.-T. Yau, Mordell-Weil Torsion, Anomalies, and Phase Transitions, 1712.02337

    arXiv

  25. [32]

    Jefferson, S

    P. Jefferson, S. Katz, H.-C. Kim and C. Vafa, On Geometric Classification of 5d SCFTs , JHEP 04 (2018) 103, [ 1801.04036]

    2018 arXiv

  26. [33]

    Apruzzi, C

    F. Apruzzi, C. Lawrie, L. Lin, S. Schafer-Nameki and Y.-N. Wang, Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States , JHEP 11 (2019) 068, [1907.05404]

    2019 arXiv

  27. [34]

    Apruzzi, C

    F. Apruzzi, C. Lawrie, L. Lin, S. Sch¨ afer-Nameki and Y.-N. Wang, Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities , JHEP 03 (2020) 052, [ 1909.09128]

    2020 arXiv

  28. [35]

    Saxena, Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study, JHEP 04 (2020) 198, [ 1911.09574]

    V. Saxena, Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study, JHEP 04 (2020) 198, [ 1911.09574]. – 90 –

    2020 arXiv

  29. [36]

    Apruzzi, S

    F. Apruzzi, S. Schafer-Nameki and Y.-N. Wang, 5d SCFTs from Decoupling and Gluing , JHEP 08 (2020) 153, [ 1912.04264]

    2020 arXiv

  30. [37]

    Collinucci and R

    A. Collinucci and R. Valandro, The role of U(1)’s in 5d theories, Higgs branches, and geometry, JHEP 10 (2020) 178, [ 2006.15464]

    2020 arXiv

  31. [38]

    Closset, S

    C. Closset, S. Schafer-Nameki and Y.-N. Wang, Coulomb and Higgs Branches from Canonical Singularities: Part 0 , JHEP 02 (2021) 003, [ 2007.15600]

    2021 arXiv

  32. [39]

    Eckhard, S

    J. Eckhard, S. Sch¨ afer-Nameki and Y.-N. Wang,Trifectas for tn in 5d , Journal of High Energy Physics 2020 (Jul, 2020)

    2020

  33. [40]

    Acharya, N

    B. Acharya, N. Lambert, M. Najjar, E. E. Svanes and J. Tian, Gauging discrete symmetries of T N -theories in five dimensions , JHEP 04 (2022) 114, [ 2110.14441]

    2022 arXiv

  34. [41]

    Tian and Y.-N

    J. Tian and Y.-N. Wang, 5D and 6D SCFTs from C3 orbifolds, SciPost Phys. 12 (2022) 127, [2110.15129]

    2022 arXiv

  35. [42]

    Closset, S

    C. Closset, S. Sch¨ afer-Nameki and Y.-N. Wang,Coulomb and Higgs branches from canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions , JHEP 04 (2022) 061, [ 2111.13564]

    2022 arXiv

  36. [43]

    De Marco, A

    M. De Marco, A. Sangiovanni and R. Valandro, 5d Higgs branches from M-theory on quasi-homogeneous cDV threefold singularities, JHEP 10 (2022) 124, [ 2205.01125]

    2022 arXiv

  37. [44]

    Mu, Y.-N

    J. Mu, Y.-N. Wang and H. N. Zhang, 5d SCFTs from isolated complete intersection singularities, JHEP 02 (2024) 155, [ 2311.05441]

    2024 arXiv

  38. [45]

    De Marco, M

    M. De Marco, M. Del Zotto, M. Graffeo and A. Sangiovanni, Conformal matter , JHEP 05 (2024) 306, [ 2311.04984]

    2024 arXiv

  39. [46]

    Alexeev, H

    V. Alexeev, H. Arg¨ uz and P. Bousseau,Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs, 2410.04714

  40. [47]

    Witten, AdS / CFT correspondence and topological field theory , JHEP 12 (1998) 012, [hep-th/9812012]

    E. Witten, AdS / CFT correspondence and topological field theory , JHEP 12 (1998) 012, [hep-th/9812012]

    1998 arXiv

  41. [48]

    I. n. Garc ´ ıa Etxebarria, B. Heidenreich and D. Regalado,IIB flux non-commutativity and the global structure of field theories , JHEP 10 (2019) 169, [ 1908.08027]

    2019 arXiv

  42. [49]

    Apruzzi, F

    F. Apruzzi, F. Bonetti, I. n. Garc ´ ıa Etxebarria, S. S. Hosseini and S. Schafer-Nameki, Symmetry TFTs from String Theory , Commun. Math. Phys. 402 (2023) 895–949, [2112.02092]

    2023 arXiv

  43. [50]

    Hubner, D

    M. Hubner, D. R. Morrison, S. Schafer-Nameki and Y.-N. Wang, Generalized Symmetries in F-theory and the Topology of Elliptic Fibrations , SciPost Phys. 13 (2022) 030, [2203.10022]

    2022 arXiv

  44. [51]

    Del Zotto, I

    M. Del Zotto, I. n. Garc ´ ıa Etxebarria and S. Schafer-Nameki,2-Group Symmetries and M-Theory, SciPost Phys. 13 (2022) 105, [ 2203.10097]

    2022 arXiv

  45. [52]

    Apruzzi, I

    F. Apruzzi, I. Bah, F. Bonetti and S. Schafer-Nameki, Noninvertible Symmetries from Holography and Branes, Phys. Rev. Lett. 130 (2023) 121601, [ 2208.07373]

    2023 arXiv

  46. [53]

    van Beest, D

    M. van Beest, D. S. W. Gould, S. Schafer-Nameki and Y.-N. Wang, Symmetry TFTs for 3d QFTs from M-theory , JHEP 02 (2023) 226, [ 2210.03703]

    2023 arXiv

  47. [54]

    J. J. Heckman, M. Hubner, E. Torres, X. Yu and H. Y. Zhang, Top down approach to topological duality defects, Phys. Rev. D 108 (2023) 046015, [ 2212.09743]. – 91 –

    2023 arXiv

  48. [55]

    Apruzzi, F

    F. Apruzzi, F. Bonetti, D. S. W. Gould and S. Schafer-Nameki, Aspects of categorical symmetries from branes: SymTFTs and generalized charges , SciPost Phys. 17 (2024) 025, [2306.16405]

    2024 arXiv

  49. [56]

    Baume, J

    F. Baume, J. J. Heckman, M. H¨ ubner, E. Torres, A. P. Turner and X. Yu, SymTrees and Multi-Sector QFTs, Phys. Rev. D 109 (2024) 106013, [ 2310.12980]

    2024 arXiv

  50. [57]

    Del Zotto, S

    M. Del Zotto, S. N. Meynet and R. Moscrop, Remarks on geometric engineering, symmetry TFTs and anomalies , JHEP 07 (2024) 220, [ 2402.18646]

    2024 arXiv

  51. [58]

    I. n. Garc ´ ıa Etxebarria and S. S. Hosseini,Some aspects of symmetry descent , JHEP 12 (2025) 223, [ 2404.16028]

    2025 arXiv

  52. [59]

    Franco and X

    S. Franco and X. Yu, Generalized symmetries in 2D from string theory: SymTFTs, intrinsic relativeness, and anomalies of non-invertible symmetries , JHEP 11 (2024) 004, [2404.19761]

    2024 arXiv

  53. [60]

    Cvetiˇ c, R

    M. Cvetiˇ c, R. Donagi, J. J. Heckman, M. H¨ ubner and E. Torres,Cornering Relative Symmetry Theories, 2408.12600

    arXiv

  54. [61]

    Tian and Y.-N

    J. Tian and Y.-N. Wang, A Tale of Bulk and Branes: Symmetry TFT of 6D SCFTs from IIB/F-theory, 2410.23076

    arXiv

  55. [62]

    Cvetiˇ c, M

    M. Cvetiˇ c, M. Dierigl, L. Lin, E. Torres and H. Y. Zhang, Frozen generalized symmetries, Phys. Rev. D 111 (2025) 026018, [ 2410.07318]

    2025 arXiv

  56. [63]

    Gagliano and I

    F. Gagliano and I. n. Garc ´ ıa Etxebarria,SymTFTs for U (1) symmetries from descent , 2411.15126

    arXiv

  57. [64]

    Gukov, P.-S

    S. Gukov, P.-S. Hsin and D. Pei, Generalized global symmetries of T [M ] theories. Part I , JHEP 04 (2021) 232, [ 2010.15890]

    2021 arXiv

  58. [65]

    Bashmakov, M

    V. Bashmakov, M. Del Zotto and A. Hasan, On the 6d origin of non-invertible symmetries in 4d , JHEP 09 (2023) 161, [ 2206.07073]

    2023 arXiv

  59. [66]

    Antinucci, C

    A. Antinucci, C. Copetti, G. Galati and G. Rizi, “Zoology” of non-invertible duality defects: the view from class S, JHEP 04 (2024) 036, [ 2212.09549]

    2024 arXiv

  60. [67]

    J. Chen, W. Cui, B. Haghighat and Y.-N. Wang, SymTFTs and duality defects from 6d SCFTs on 4-manifolds , JHEP 11 (2023) 208, [ 2305.09734]

    2023 arXiv

  61. [68]

    Bashmakov, M

    V. Bashmakov, M. Del Zotto and A. Hasan, Four-manifolds and Symmetry Categories of 2d CFTs, 2305.10422

    arXiv

  62. [69]

    W. Cui, B. Haghighat and L. Ruggeri, Non-invertible surface defects in 2+1d QFTs from half spacetime gauging , JHEP 11 (2024) 159, [ 2406.09261]

    2024 arXiv

  63. [70]

    J. Chen, W. Cui, B. Haghighat and Y. Sun, Modularity of Vafa-Witten Partition Functions from SymTFT, 2409.19397

    arXiv

  64. [71]

    C´ ordova, D

    C. C´ ordova, D. S. Freed, H. T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications I , SciPost Phys. 8 (2020) 001, [ 1905.09315]

    2020 arXiv

  65. [72]

    C´ ordova, D

    C. C´ ordova, D. S. Freed, H. T. Lam and N. Seiberg, Anomalies in the Space of Coupling Constants and Their Dynamical Applications II , SciPost Phys. 8 (2020) 002, [ 1905.13361]

    2020 arXiv

  66. [73]

    T. D. Brennan and C. Cordova, Axions, higher-groups, and emergent symmetry , JHEP 02 (2022) 145, [ 2011.09600]. – 92 –

    2022 arXiv

  67. [74]

    Aguilera Damia, R

    J. Aguilera Damia, R. Argurio and L. Tizzano, Continuous Generalized Symmetries in Three Dimensions, JHEP 23 (2023) 164, [ 2206.14093]

    2023 arXiv

  68. [75]

    Aloni, E

    D. Aloni, E. Garc ´ ıa-Valdecasas, M. Reece and M. Suzuki,Spontaneously broken (-1)-form U(1) symmetries , SciPost Phys. 17 (2024) 031, [ 2402.00117]

    2024 arXiv

  69. [76]

    Garc ´ ıa-Valdecasas, M

    E. Garc ´ ıa-Valdecasas, M. Reece and M. Suzuki,Monopole Breaking of Chern-Weil Symmetries, 2408.00067

    arXiv

  70. [77]

    T. D. Brennan, Constraints on symmetry-preserving gapped phases from coupling constant anomalies, Phys. Rev. D 110 (2024) L041701, [ 2404.11660]

    2024 arXiv

  71. [78]

    McNamara and C

    J. McNamara and C. Vafa, Baby Universes, Holography, and the Swampland , 2004.06738

    2004 arXiv

  72. [79]

    J. J. Heckman, M. H¨ ubner and C. Murdia, On the holographic dual of a topological symmetry operator, Phys. Rev. D 110 (2024) 046007, [ 2401.09538]

    2024 arXiv

  73. [80]

    Yu, Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization, JHEP 08 (2021) 061, [ 2010.01136]

    M. Yu, Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization, JHEP 08 (2021) 061, [ 2010.01136]

    2021 arXiv

  74. [81]

    Santilli and R

    L. Santilli and R. J. Szabo, Higher form symmetries and orbifolds of two-dimensional Yang–Mills theory, Lett. Math. Phys. 115 (2025) 15, [ 2403.03119]

    2025 arXiv

  75. [82]

    Vafa, Modular Invariance and Discrete Torsion on Orbifolds , Nucl

    C. Vafa, Modular Invariance and Discrete Torsion on Orbifolds , Nucl. Phys. B 273 (1986) 592–606

    1986

  76. [83]

    Hellerman, A

    S. Hellerman, A. Henriques, T. Pantev, E. Sharpe and M. Ando, Cluster decomposition, T-duality, and gerby CFT’s , Adv. Theor. Math. Phys. 11 (2007) 751–818, [hep-th/0606034]

    2007 arXiv

  77. [84]

    Sharpe, Decomposition in diverse dimensions , Phys

    E. Sharpe, Decomposition in diverse dimensions , Phys. Rev. D 90 (2014) 025030, [1404.3986]

    2014 arXiv

  78. [85]

    Sharpe, Undoing decomposition, Int

    E. Sharpe, Undoing decomposition, Int. J. Mod. Phys. A 34 (2020) 1950233, [ 1911.05080]

    2020 arXiv

  79. [86]

    Robbins, E

    D. Robbins, E. Sharpe and T. Vandermeulen, A generalization of decomposition in orbifolds, JHEP 21 (2020) 134, [ 2101.11619]

    2020 arXiv

  80. [87]

    Sharpe, Topological operators, noninvertible symmetries and decomposition, Adv

    E. Sharpe, Topological operators, noninvertible symmetries and decomposition, Adv. Theor. Math. Phys. 27 (2023) 2319–2407, [ 2108.13423]

    2023 arXiv

  81. [88]

    Pantev, D

    T. Pantev, D. G. Robbins, E. Sharpe and T. Vandermeulen, Orbifolds by 2-groups and decomposition, JHEP 09 (2022) 036, [ 2204.13708]

    2022 arXiv

  82. [89]

    Sharpe, An introduction to decomposition, in 2021-2022 MATRIX Annals , ch

    E. Sharpe, An introduction to decomposition, in 2021-2022 MATRIX Annals , ch. 8, p. 145–168. Springer Nature Switzerland, 2024. 2204.09117. DOI

    2021 arXiv

  83. [90]

    Del Zotto, J

    M. Del Zotto, J. J. Heckman, D. S. Park and T. Rudelius, On the Defect Group of a 6D SCFT, Lett. Math. Phys. 106 (2016) 765–786, [ 1503.04806]

    2016 arXiv

  84. [91]

    Albertini, M

    F. Albertini, M. Del Zotto, I. n. Garc ´ ıa Etxebarria and S. S. Hosseini, Higher Form Symmetries and M-theory , JHEP 12 (2020) 203, [ 2005.12831]

    2020 arXiv

  85. [92]

    Yu, Gauging in Parameter Space: A Top-Down Perspective , 2411.14997

    X. Yu, Gauging in Parameter Space: A Top-Down Perspective , 2411.14997

    arXiv

  86. [93]

    T. D. Brennan and Z. Sun, A SymTFT for continuous symmetries , JHEP 12 (2024) 100, [2401.06128]

    2024 arXiv

  87. [94]

    Antinucci and F

    A. Antinucci and F. Benini, Anomalies and gauging of U(1) symmetries , Phys. Rev. B 111 (2025) 024110, [ 2401.10165]. – 93 –

    2025 arXiv

  88. [95]

    Apruzzi, F

    F. Apruzzi, F. Bedogna and N. Dondi, SymTh for non-finite symmetries , 2402.14813

  89. [96]

    J. J. Heckman, M. H¨ ubner, E. Torres and H. Y. Zhang, The Branes Behind Generalized Symmetry Operators, Fortsch. Phys. 71 (2023) 2200180, [ 2209.03343]

    2023 arXiv

  90. [97]

    Cvetiˇ c, J

    M. Cvetiˇ c, J. J. Heckman, M. H¨ ubner and E. Torres,Fluxbranes, generalized symmetries, and Verlinde’s metastable monopole , Phys. Rev. D 109 (2024) 046007, [ 2305.09665]

    2024 arXiv

  91. [98]

    Bergman, E

    O. Bergman, E. Garcia-Valdecasas, F. Mignosa and D. Rodriguez-Gomez, Non-BPS branes and continuous symmetries , 2407.00773

    arXiv

  92. [99]

    E. R. Sharpe, Analogues of discrete torsion for the M theory three form , Phys. Rev. D 68 (2003) 126004, [ hep-th/0008170]

    2003 arXiv

  93. [100]

    R. L. Bryant and S. M. Salamon, On the construction of some complete metrics with exceptional holonomy, Duke Mathematical Journal 58 (1989) 829 – 850

    1989

  94. [101]

    D. R. Morrison, S. Schafer-Nameki and B. Willett, Higher-Form Symmetries in 5d , JHEP 09 (2020) 024, [ 2005.12296]

    2020 arXiv

  95. [102]

    Bhardwaj and S

    L. Bhardwaj and S. Sch¨ afer-Nameki,Higher-form symmetries of 6d and 5d theories , JHEP 02 (2021) 159, [ 2008.09600]

    2021 arXiv

  96. [103]

    Bhardwaj, Flavor symmetry of 5d SCFTs

    L. Bhardwaj, Flavor symmetry of 5d SCFTs. Part I. General setup , JHEP 09 (2021) 186, [2010.13230]

    2021 arXiv

  97. [104]

    Bhardwaj, Flavor symmetry of 5 d SCFTs

    L. Bhardwaj, Flavor symmetry of 5 d SCFTs. Part II. Applications , JHEP 04 (2021) 221, [2010.13235]

    2021 arXiv

  98. [105]

    Apruzzi, S

    F. Apruzzi, S. Schafer-Nameki, L. Bhardwaj and J. Oh, The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs , SciPost Phys. 13 (2022) 024, [2105.08724]

    2022 arXiv

  99. [106]

    P. B. Genolini and L. Tizzano, Comments on Global Symmetries and Anomalies of 5d SCFTs, Commun. Math. Phys. 405 (2024) 255, [ 2201.02190]

    2024 arXiv

  100. [107]

    Brandhuber, J

    A. Brandhuber, J. Gomis, S. S. Gubser and S. Gukov, Gauge theory at large N and new G(2) holonomy metrics , Nucl. Phys. B 611 (2001) 179–204, [ hep-th/0106034]

    2001 arXiv

  101. [108]

    C´ ordova, T

    C. C´ ordova, T. T. Dumitrescu and K. Intriligator, Exploring 2-Group Global Symmetries , JHEP 02 (2019) 184, [ 1802.04790]

    2019 arXiv

  102. [109]

    Benini, C

    F. Benini, C. C´ ordova and P.-S. Hsin,On 2-Group Global Symmetries and their Anomalies , JHEP 03 (2019) 118, [ 1803.09336]

    2019 arXiv

  103. [110]

    Hidaka, M

    Y. Hidaka, M. Nitta and R. Yokokura, Global 3-group symmetry and ’t Hooft anomalies in axion electrodynamics, JHEP 01 (2021) 173, [ 2009.14368]

    2021 arXiv

  104. [111]

    Hidaka, M

    Y. Hidaka, M. Nitta and R. Yokokura, Global 4-group symmetry and ’t Hooft anomalies in topological axion electrodynamics, PTEP 2022 (2022) 04A109, [ 2108.12564]

    2022 arXiv

  105. [112]

    Bhardwaj and D

    L. Bhardwaj and D. S. W. Gould, Disconnected 0-form and 2-group symmetries , JHEP 07 (2023) 098, [ 2206.01287]

    2023 arXiv

  106. [113]

    Copetti, M

    C. Copetti, M. Del Zotto, K. Ohmori and Y. Wang, Higher Structure of Chiral Symmetry , 2305.18282

    arXiv

  107. [114]

    M. J. Kang and S. Kang, Central extensions of higher groups: Green-Schwarz mechanism and 2-connections, 2311.14666. – 94 –

    arXiv

  108. [115]

    R. Liu, R. Luo and Y.-N. Wang, Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries, 2406.03974

    arXiv

  109. [117]

    Seiberg, Modifying the Sum Over Topological Sectors and Constraints on Supergravity , JHEP 07 (2010) 070, [ 1005.0002]

    N. Seiberg, Modifying the Sum Over Topological Sectors and Constraints on Supergravity , JHEP 07 (2010) 070, [ 1005.0002]

    2010 arXiv

  110. [118]

    M. J. Hopkins and I. M. Singer, Quadratic functions in geometry, topology, and M theory , J. Diff. Geom. 70 (2005) 329–452, [ math/0211216]

    2005 arXiv

  111. [119]

    Cheeger and J

    J. Cheeger and J. Simons, Differential characters and geometric invariants , in Geometry and topology (College Park, Md., 1983/84) , vol. 1167 of Letc. Notes Math. , pp. 50–80. Springer, 1985

    1983

  112. [120]

    Bar and C

    C. Bar and C. Becker, Differential Characters, vol. 2112 of Letc. Notes Phys. Springer, 2014, 10.1007/978-3-319-07034-6

    2014 doi

  113. [121]

    D. S. Freed, G. W. Moore and G. Segal, Heisenberg Groups and Noncommutative Fluxes , Annals Phys. 322 (2007) 236–285, [ hep-th/0605200]

    2007 arXiv

  114. [122]

    R. J. Szabo, Quantization of Higher Abelian Gauge Theory in Generalized Differential Cohomology, PoS ICMP2012 (2012) 009, [ 1209.2530]

    2012 arXiv

  115. [123]

    Gutperle and A

    M. Gutperle and A. Strominger, Fluxbranes in string theory , JHEP 06 (2001) 035, [hep-th/0104136]

    2001 arXiv

  116. [124]

    D. N. Page, Classical Stability of Round and Squashed Seven Spheres in Eleven-dimensional Supergravity, Phys. Rev. D 28 (1983) 2976

    1983

  117. [125]

    P. S. Howe, E. Sezgin and P. C. West, The Six-dimensional selfdual tensor , Phys. Lett. B 400 (1997) 255–259, [ hep-th/9702111]

    1997 arXiv

  118. [126]

    I. A. Bandos, K. Lechner, A. Nurmagambetov, P. Pasti, D. P. Sorokin and M. Tonin, Covariant action for the superfive-brane of M theory , Phys. Rev. Lett. 78 (1997) 4332–4334, [hep-th/9701149]

    1997 arXiv

  119. [127]

    K. A. Intriligator, Anomaly matching and a Hopf-Wess-Zumino term in 6d, N=(2,0) field theories, Nucl. Phys. B 581 (2000) 257–273, [ hep-th/0001205]

    2000 arXiv

  120. [128]

    Pilch, A

    K. Pilch, A. Tyukov and N. P. Warner, Flowing to Higher Dimensions: A New Strongly-Coupled Phase on M2 Branes , JHEP 11 (2015) 170, [ 1506.01045]

    2015 arXiv

  121. [129]

    Anabal´ on, M

    A. Anabal´ on, M. Chamorro-Burgos and A. Guarino, Janus and Hades in M-theory , JHEP 11 (2022) 150, [ 2207.09287]

    2022 arXiv

  122. [130]

    Fiorenza, H

    D. Fiorenza, H. Sati and U. Schreiber, Twisted Cohomotopy implies level quantization of the full 6d Wess-Zumino term of the M5-brane , Commun. Math. Phys. 384 (2021) 403–432, [1906.07417]

    2021 arXiv

  123. [131]

    G. W. Moore, Anomalies, Gauss laws, and Page charges in M-theory , Comptes Rendus Physique 6 (2005) 251–259, [ hep-th/0409158]

    2005 arXiv

  124. [132]

    Bonetti, M

    F. Bonetti, M. Del Zotto and R. Minasian, SymTFTs for Continuous non-Abelian Symmetries, 2402.12347

  125. [133]

    C. T. C. Wall, Classification problems in differential topology. V , Invent. Math. 1 (1966) 355–374. – 95 –

    1966

  126. [134]

    Kapustin and N

    A. Kapustin and N. Seiberg, Coupling a QFT to a TQFT and Duality , JHEP 04 (2014) 001, [1401.0740]

    2014 arXiv

  127. [135]

    Bhardwaj, S

    L. Bhardwaj, S. Schafer-Nameki and A. Tiwari, Unifying constructions of non-invertible symmetries, SciPost Phys. 15 (2023) 122, [ 2212.06159]

    2023 arXiv

  128. [136]

    Banerjee, P

    S. Banerjee, P. Longhi and M. Romo, Exploring 5d BPS Spectra with Exponential Networks , Annales Henri Poincare 20 (2019) 4055–4162, [ 1811.02875]

    2019 arXiv

  129. [137]

    Banerjee, P

    S. Banerjee, P. Longhi and M. Romo, Exponential BPS Graphs and D Brane Counting on Toric Calabi-Yau Threefolds: Part I , Commun. Math. Phys. 388 (2021) 893–945, [1910.05296]

    2021 arXiv

  130. [138]

    Banerjee, P

    S. Banerjee, P. Longhi and M. Romo, Exponential BPS graphs and D-brane counting on toric Calabi-Yau threefolds: Part II , 2012.09769

    2012 arXiv

  131. [139]

    Santilli and C

    L. Santilli and C. F. Uhlemann, 3d defects in 5d: RG flows and defect F-maximization , JHEP 06 (2023) 136, [ 2305.01004]

    2023 arXiv

  132. [140]

    Benetti Genolini and L

    P. Benetti Genolini and L. Tizzano, Instantons, symmetries and anomalies in five dimensions, JHEP 04 (2021) 188, [ 2009.07873]

    2021 arXiv

  133. [141]

    Del Zotto, J

    M. Del Zotto, J. J. Heckman, S. N. Meynet, R. Moscrop and H. Y. Zhang, Higher symmetries of 5D orbifold SCFTs , Phys. Rev. D 106 (2022) 046010, [ 2201.08372]

    2022 arXiv

  134. [142]

    S.-T. Yau, S. S.-T. Yau and Y. Yu, Gorenstein quotient singularities in dimension three , vol. 505. American Mathematical Soc., 1993

    1993

  135. [143]

    M. A. Armstrong, The fundamental group of the orbit space of a discontinuous group , Mathematical Proceedings of the Cambridge Philosophical Society 64 (1968) 299 – 301

    1968

  136. [144]

    M. A. M. Najjar, Field Theory Dynamics from M-theory on Special Holonomy Manifolds . PhD thesis, King’s Coll. London, 2022

    2022

  137. [145]

    Y. V. Bazaikin and O. A. Bogoyavlenskaya, Complete Riemannian G2 Holonomy Metrics on Deformations of Cones over S3 x S3 , 1301.6379

    arXiv

  138. [146]

    Foscolo, M

    L. Foscolo, M. Haskins and J. Nordstr¨ om,Infinitely many new families of complete cohomogeneity one G 2-manifolds: G 2 analogues of the Taub–NUT and Eguchi–Hanson spaces, J. Eur. Math. Soc. 23 (2021) 2153–2220, [ 1805.02612]

    2021 arXiv

  139. [147]

    Friedmann, On the quantum moduli space of M theory compactifications , Nucl

    T. Friedmann, On the quantum moduli space of M theory compactifications , Nucl. Phys. B 635 (2002) 384–394, [ hep-th/0203256]

    2002 arXiv

  140. [148]

    Friedmann and R

    T. Friedmann and R. P. Stanley, The String Landscape: On Formulas for Counting Vacua , Nucl. Phys. B 869 (2013) 74–88, [ 1212.0583]

    2013 arXiv

  141. [149]

    Cort´ es and J

    V. Cort´ es and J. J. V´ asquez,Locally homogeneous nearly K¨ ahler manifolds, Annals of Global Analysis and Geometry 48 (2015) 269–294, [ 1410.6912]

    2015 arXiv

  142. [150]

    Cachazo, N

    F. Cachazo, N. Seiberg and E. Witten, Phases of N=1 supersymmetric gauge theories and matrices, JHEP 02 (2003) 042, [ hep-th/0301006]

    2003 arXiv

  143. [151]

    Hosomichi and D

    K. Hosomichi and D. C. Page, G(2) holonomy, mirror symmetry and phases of N=1 SYM , JHEP 05 (2005) 041, [ hep-th/0501195]

    2005 arXiv

  144. [152]

    Davies, Hyperconifold Transitions, Mirror Symmetry, and String Theory , Nucl

    R. Davies, Hyperconifold Transitions, Mirror Symmetry, and String Theory , Nucl. Phys. B 850 (2011) 214–231, [ 1102.1428]. – 96 –

    2011 arXiv

  145. [153]

    Davies, Classification and Properties of Hyperconifold Singularities and Transitions , 1309.6778

    R. Davies, Classification and Properties of Hyperconifold Singularities and Transitions , 1309.6778

    arXiv

  146. [154]

    Gaiotto, A

    D. Gaiotto, A. Kapustin, Z. Komargodski and N. Seiberg, Theta, Time Reversal, and Temperature, JHEP 05 (2017) 091, [ 1703.00501]

    2017 arXiv

  147. [155]

    Gaiotto, Z

    D. Gaiotto, Z. Komargodski and N. Seiberg, Time-reversal breaking in QCD 4, walls, and dualities in 2 + 1 dimensions , JHEP 01 (2018) 110, [ 1708.06806]

    2018 arXiv

  148. [156]

    Pantev and E

    T. Pantev and E. Sharpe, Notes on gauging noneffective group actions , hep-th/0502027

    arXiv

  149. [157]

    Pantev and E

    T. Pantev and E. Sharpe, String compactifications on Calabi-Yau stacks , Nucl. Phys. B 733 (2006) 233–296, [ hep-th/0502044]

    2006 arXiv

  150. [158]

    Pantev and E

    T. Pantev and E. Sharpe, GLSM’s for Gerbes (and other toric stacks) , Adv. Theor. Math. Phys. 10 (2006) 77–121, [ hep-th/0502053]

    2006 arXiv

  151. [159]

    Bunke, Differential cohomology, 1208.3961

    U. Bunke, Differential cohomology, 1208.3961

    arXiv

  152. [160]

    Simons and D

    J. Simons and D. Sullivan, Axiomatic characterization of ordinary differential cohomology , Journal of Topology 1 (Oct., 2007) 45–56, [ math/0701077]

    2007 arXiv

  153. [161]

    Cvetic, M

    M. Cvetic, M. Dierigl, L. Lin and H. Y. Zhang, Higher-form symmetries and their anomalies in M-/F-theory duality , Phys. Rev. D 104 (2021) 126019, [ 2106.07654]

    2021 arXiv

  154. [162]

    Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries , Phys

    S. Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries , Phys. Rept. 1063 (2024) 1–55, [ 2305.18296]

    2024 arXiv

  155. [163]

    T. D. Brennan and S. Hong, Introduction to Generalized Global Symmetries in QFT and Particle Physics , 2306.00912

    arXiv

  156. [164]

    Luo, Q.-R

    R. Luo, Q.-R. Wang and Y.-N. Wang, Lecture notes on generalized symmetries and applications, Phys. Rept. 1065 (2024) 1–43, [ 2307.09215]

    2024 arXiv

  157. [165]

    Bhardwaj, L

    L. Bhardwaj, L. E. Bottini, L. Fraser-Taliente, L. Gladden, D. S. W. Gould, A. Platschorre et al., Lectures on generalized symmetries, Phys. Rept. 1051 (2024) 1–87, [ 2307.07547]

    2024 arXiv

  158. [166]

    Shao, What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries, 2308.00747

    S.-H. Shao, What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries, 2308.00747

    arXiv

  159. [167]

    Iqbal, Jena lectures on generalized global symmetries: principles and applications , 2407.20815

    N. Iqbal, Jena lectures on generalized global symmetries: principles and applications , 2407.20815

    arXiv

  160. [168]

    D. S. Freed, G. W. Moore and C. Teleman, Topological symmetry in quantum field theory , 2209.07471

    arXiv

  161. [169]

    Birmingham, M

    D. Birmingham, M. Blau, M. Rakowski and G. Thompson, Topological field theory, Phys. Rept. 209 (1991) 129–340

    1991

  162. [170]

    Cremmer, B

    E. Cremmer, B. Julia and J. Scherk, Supergravity Theory in 11 Dimensions , Phys. Lett. B 76 (1978) 409–412

    1978

  163. [171]

    I. A. Bandos, N. Berkovits and D. P. Sorokin, Duality symmetric eleven-dimensional supergravity and its coupling to M-branes , Nucl. Phys. B 522 (1998) 214–233, [hep-th/9711055]

    1998 arXiv

  164. [172]

    D. P. Sorokin, Coupling of M-branes in M theory , in 6th International Symposium on Particles, Strings and Cosmology , pp. 697–701, 3, 1998. hep-th/9806175

    1998 arXiv

  165. [173]

    P. A. M. Dirac, The Theory of magnetic poles , Phys. Rev. 74 (1948) 817–830. – 97 –

    1948

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.