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REVIEW 4 major objections 4 minor 56 references

Adjusting Higher Chern-Simons Theory

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper shows that a consistent higher Chern-Simons theory is obtained by completing an adjusted gauge algebra to its cotangent $L_\infty$-algebra and dropping only the cotangent higher gauge transformations.

desk verdict The 4d half-adjusted construction is real and the no-go theorem is useful, but the advertised arbitrary-dimensional generalization is not yet proven. read the letter →

arxiv 2507.02082 v1 pith:7LDF6DMH submitted 2025-07-02 hep-th math-phmath.MP

Gianni Gagliardo , Dominik Rist , Christian Saemann , Martin Wolf This is my paper
classification hep-thmath-phmath.MP MSC 81T1381T4581T70
keywords higherChern-SimonstheorygaugeL-infinityalgebrasadjustedconnectionsfakeflatnessprincipal2-bundlescyclicstringLie2-algebra
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 sets out to construct higher Chern–Simons theories that are genuinely higher—involving 2-form potentials and higher gauge transformations—without being forced onto the fake-flatness constraint, the condition that all but the top curvature vanish, which would trivialise the action. Its first result is negative: a fully adjusted theory is impossible, because for a cyclic minimal non-Abelian higher gauge algebra the adjustment conditions force all higher products to be zero. The workaround is the half-adjusted theory: start with an adjusted $L_\infty$-algebra (a generalised Lie algebra with higher-arity brackets, here also equipped with an adjustment deforming its curvature), complete it to its cotangent $L_\infty$-algebra so that it carries an inner product, and use the action $S = \int (A^*\wedge H + B^*\wedge F)$ in four dimensions. This action is gauge invariant, all ordinary gauge transformations close, and the equations of motion are full flatness: $F = 0$, $F^* = 0$, $H = 0$, $H^* = 0$. The price is that the higher gauge transformations acting in the cotangent directions are set to zero by hand, and in dimensions above four the paper leaves the closure of ordinary gauge transformations open.

What carries the argument

The central object is the half-adjusted cotangent $L_\infty$-algebra. Starting from an adjusted $n$-term $L_\infty$-algebra $L$ with adjustment $\kappa$, one passes to the degree-shifted cotangent algebra $T^*[n-1]L = L \oplus L^*[n-1]$, whose canonical pairing provides the cyclic (inner product) structure that adjusted non-Abelian algebras generically lack. The adjustment $\kappa$ deforms the curvature $H$ and the gauge transformations of the $L$-valued fields, while the cotangent directions supply the dual fields $A^*, B^*$ and curvatures $F^*, H^*$. The relation $d(A^*\wedge H + B^*\wedge F) = F^*\wedge H + H^*\wedge F$ fixes those dual curvatures and guarantees gauge invariance of the action; the restriction $\theta = (\theta, 0)$ to base-direction higher gauge transformations removes the only non-closing symmetries.

What would settle it

Compute the BRST cohomology of the four-dimensional half-adjusted complex with the cotangent higher-gauge ghosts set to zero; if a non-trivial cohomology class depends on those excluded ghosts, the truncation removes physical states. Alternatively, produce any explicit adjusted $L_\infty$-algebra in dimension $d > 4$ for which ordinary gauge transformations fail to close, which would show the higher-dimensional generalisation does not hold as stated.

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Extended reading notes

Core claim

The central discovery is that the fake-flatness obstruction in higher Chern–Simons theory can be avoided by a half-adjustment rather than a full one. A full adjustment would deform the curvatures of an $L_\infty$-connection so that all higher gauge transformations close, but Theorem 3.2 shows that a cyclic adjusted minimal $n$-term $L_\infty$-algebra with $n > 1$ is Abelian; since quasi-isomorphic gauge $L_\infty$-algebras give semi-classically equivalent theories, this rules out the fully adjusted construction for non-Abelian algebras. The paper's solution starts from an adjusted algebra $L$, such as the string Lie 2-algebra, and forms its cotangent completion $T^*[n-1]L$, which is cyclic by construction. In four dimensions the field content is $(A, B)$ in $L$ together with dual fields $(A^*, B^*)$, the action is $S = \int (A^*\wedge H + B^*\wedge F)$, the ordinary gauge transformations close on all fields, and the equations of motion are $F = 0$, $F^* = 0$, $H = 0$, $H^* = 0$. The higher gauge transformations in the cotangent directions fail to close and are excluded by setting their parameter to zero; the paper argues this is a mild restriction and backs it with finite gauge transformations and a complete differential-cocycle description of principal 2-bundles with half-adjusted connections.

Load-bearing premise

The load-bearing premise is that discarding the higher gauge transformations in the cotangent directions, by setting their parameter $\theta^*$ to zero, removes no physical degrees of freedom; if this truncation is not innocuous the theory is not the higher Chern–Simons theory it claims to be.

Editorial extensions

If this is right

  • In four dimensions the half-adjusted equations of motion are $F = 0$, $F^* = 0$, $H = 0$ and $H^* = 0$, so every solution is a fully flat 2-connection, the expected on-shell content of a higher Chern–Simons theory.
  • Ordinary gauge transformations close off-shell without any fake-flatness condition; the construction removes only the higher gauge transformations acting along the cotangent directions.
  • The differential cohomology of principal 2-bundles with half-adjusted connections is fully spelled out, including cocycle and coboundary relations, so the theory can be formulated globally on nontrivial bundles.
  • A fully adjusted non-Abelian higher Chern–Simons theory cannot exist within cyclic minimal $n$-term $L_\infty$-algebras, so the half-adjusted construction is the only current route of this type.
  • The higher-dimensional analogue has the same action principle, but the paper leaves the closure of ordinary gauge transformations in dimensions greater than four as an open question.

Reading between the lines

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

  • A direct test of the truncation would be a BRST cohomology computation with the cotangent higher-gauge ghosts set to zero; if those excluded ghosts carry non-trivial cohomology classes, the truncation would alter the physical state space rather than merely remove redundancies.
  • The cotangent-completion step is likely transferable to other theories whose action pairs a connection with a curvature, potentially yielding cyclic gauge algebras for BF-type theories and tensor hierarchies.
  • Because the on-shell condition is full flatness, the four-dimensional theory is naturally a theory of flat 2-connections; a longer-term probe would be whether it produces invariants of higher-dimensional knots or bordisms, mirroring the role of ordinary Chern–Simons theory in knot theory.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes 'half-adjusted higher Chern-Simons theories' as a way around the fake-flatness obstruction. After reviewing L∞-algebras and homotopy Maurer-Cartan Chern-Simons theory, it proves (or sketches) a no-go theorem that cyclic adjusted skeletal n-term L∞-algebras are Abelian (Theorem 3.2). The main construction is the cotangent completion of an adjusted 2-term L∞-algebra: in four dimensions the authors write the action S = ∫(A*∧H + B*∧F), verify that ordinary gauge transformations close (Eq. (4.13)), that all curvatures vanish on-shell (Eq. (4.11)), and that higher gauge transformations close only after truncating the cotangent directions by setting θ* = 0 (Eqs. (4.14)-(4.15)). They also develop finite gauge transformations and the differential cohomology of principal 2-bundles with half-adjusted connections. Section 4.3 sketches a higher-dimensional generalisation, and Section 5 compares the approach with adding trivial symmetries.

Significance. If the four-dimensional construction is taken as the main result, this is a valuable contribution: it gives an explicit, internally consistent higher Chern-Simons theory whose equations of motion imply full flatness, and it supplies a concrete differential-cohomological description of the relevant 2-bundles. The no-go theorem, if fully proven, is also significant for the programme of adjusted higher gauge theory. The paper's strengths include the explicit verification of gauge invariance and closure in Section 4.1, the careful finite treatment in Section 4.2, and the honest identification of the limitations of the higher-dimensional generalisation in Section 4.3. However, the abstract and introduction claim a general construction in arbitrary dimensions, whereas the text itself concedes that closure of ordinary gauge transformations is unproved for d > 4. The significance of the paper therefore depends on whether the general claims can be either established or substantially scaled back to the four-dimensional case.

major comments (4)
  1. [§4.3, final paragraph] The abstract states that the authors 'develop the general construction of these theories in arbitrary dimensions', and expectation (i) in Section 1 requires a higher gauge theory whose gauge and higher gauge transformations act consistently. But §4.3 explicitly says: 'it is not possible to make any definite statement about closure of even ordinary gauge transformations in the higher case.' This is a load-bearing gap: without closure there is no well-defined gauge theory in d > 4. The authors should either prove closure for a specified class of adjusted algebras (for example, strict algebras with at most binary adjustment automorphisms) or explicitly restrict the paper's central claim to d = 4 and present the higher-dimensional discussion as an outlook.
  2. [§4.3, Eqs. (4.40)-(4.51)] The claim that the equations of motion reproduce total flatness in arbitrary dimensions is not established. The variation computation leading to (4.44) is an identity for δS, but the term R*_A is only said to contain 'at least one curvature form of lower degree'. No argument is given that the resulting equations of motion force each curvature F^A and F*_A to vanish individually, nor is an induction on form degree supplied. In d = 4 the equations of motion (4.11) are checked directly, so the four-dimensional result is safe, but expectation (ii) for the general construction remains open.
  3. [§4.3, Eqs. (4.37b), (4.41), (4.53)] The higher-dimensional curvature forms F*_A are not uniquely determined by the construction. Equation (4.41) determines them only up to the terms (4.53), which may contain arbitrary powers of the connection generators, and the deformation parameters λ and ρ in (4.37b) are correspondingly left unspecified. The text acknowledges that different choices lead to equivalent descriptions, but no equivalence statement is proven. Consequently, the higher-dimensional gauge structure is not uniquely defined by the proposed construction, which undermines the claim of a 'general construction' in arbitrary dimensions.
  4. [§4.1, Eqs. (4.14)-(4.15)] The truncation of higher gauge transformations to θ* = 0 is a consistent definitional choice, but the paper does not justify the claim that this is only a 'mild restriction' that does not remove physical degrees of freedom. In particular, no proof is given that the excluded cotangent-direction higher gauge transformations decouple from the action or from the on-shell degrees of freedom. Since this truncation is part of the definition of 'half-adjusted theory' in all dimensions, its physical innocuousness should either be demonstrated or clearly stated as an assumption, rather than presented as an automatic consequence of the construction.
minor comments (4)
  1. [§4.1, Eq. (4.15b)] The displayed equation 'δB = µ2(F,θ)+κ(µ1(θ),F) = 0' is easy to misread as an inconsistency with the following '≠ 0' for δB*. Please add a short remark that the first equality follows from the adjustment condition (3.9), and consider writing the two equations with explicit '= 0' and '≠ 0' separated for clarity.
  2. [§1, paragraph introducing [30,31]] The sentence 'one would expect Lax connections for a p(d+1)-dimensional integrable field theory to involve a d-form' appears garbled; it should presumably read 'a (d+1)-dimensional integrable field theory to involve a d-form'.
  3. [§3.2, proof of Theorem 3.2] The proof of Theorem 3.2 is very compressed, especially the step 'Considering (3.18) for i ≥ 3 then shows similarly that all the higher products vanish'. Since this theorem is a central no-go statement, please expand this argument or cite a source containing the full proof.
  4. [§4.2, Eq. (4.27)] The expression for F̃* in Eq. (4.27) has unbalanced parentheses around the term with t*(...). Please correct the typesetting so that the bracketing is unambiguous.

Circularity Check

0 steps flagged · score 2.0 of 10

No substantive circularity: the 4d half-adjusted construction is independently verified; a minor self-citation (Proposition 3.1 from [46]) is supported by an included proof.

full rationale

The central derivation is not a re-derivation of its inputs. Theorem 2.1 (quasi-isomorphic gauge L8-algebras yield semi-classically equivalent higher Chern-Simons theories) is proved in the paper, and the 4d half-adjusted construction in Section 4.1 is verified by explicit computation: ordinary gauge transformations close in (4.13), the higher-gauge obstruction is isolated in (4.15b), and the excluded cotangent-direction higher transformations are identified as theta* = 0. Proposition 3.1, cited from the authors' earlier [46], is the only notable self-citation; it is not load-bearing in a circular way because the present paper reproduces its derivation in Appendix A and the subsequent no-go theorem (Theorem 3.2) applies the stated adjustment conditions rather than relying on the citation as an unverified premise. The admission in Section 4.3 that 'it is not possible to make any definite statement about closure of even ordinary gauge transformations in the higher case' is a genuine limitation of the arbitrary-dimensional generality claim, but a limitation is not circularity. The score reflects one minor self-citation that is not load-bearing; no prediction reduces by construction to a fitted input.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central claim depends on standard L8-algebra and BV formalism background, plus domain assumptions about the desired form of higher Chern-Simons theories and the validity of the descent condition. The manual truncation θ* = 0 is a clear ad hoc choice. No new physical entities are postulated.

free parameters (2)
  • cotangent-direction higher gauge transformations θ* = 0 (truncated)
    The consistency of the half-adjusted theory relies on setting the higher gauge transformations in the cotangent directions to zero by hand (Section 4.1). This is a manual restriction, not derived from the algebraic structure.
  • deformation parameters λ, ρ in higher-dimensional curvature F*_A = unspecified
    In the higher-dimensional generalisation (4.37b), the additional curvature forms are fixed by (4.41) only up to the parameters λ and ρ, which are left unspecified; different choices are claimed to be equivalent (Section 4.3).
assumptions (6)
  • standard math Minimal model theorem: any L8-algebra is quasi-isomorphic to a minimal one.
    Used in Section 2.3 to reduce higher Chern-Simons theories to minimal models, enabling the no-go theorem.
  • standard math The BV complex of a field theory is encoded by an L8-algebra, and quasi-isomorphic L8-algebras give equivalent tree-level S-matrices.
    Invoked to prove Theorem 2.1 (semi-classical equivalence) in Section 2.3, cited to [38].
  • domain assumption The three expectations (i)-(iii) for interesting higher Chern-Simons theories are adopted as design goals.
    Stated in Section 1; they define what counts as a desirable theory and are not derived from more basic principles.
  • domain assumption Principal higher bundles are restricted to be topologically trivial.
    Stated in Section 1: 'as common in the discussion of Chern-Simons theory, we will restrict ourselves here to higher principal bundles which are topologically trivial.'
  • domain assumption The descent condition d(A* F) = F* F fixes the additional curvature forms and ensures gauge invariance.
    Introduced in Section 4.1 (Eq. 4.8) and generalised in Eq. (4.41); the definition of F* and the gauge invariance of the action rest on this condition.
  • ad hoc to paper The manual restriction of higher gauge transformations to θ* = 0 is consistent and physically innocuous.
    Introduced in Section 4.1: 'we have to restrict higher gauge transformations to those that are parametrised by θ=(θ,0).' This is the load-bearing assumption that makes the half-adjusted theory work.

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Cite this review

Pith. "Pith review of Adjusting Higher Chern-Simons Theory." pith.science (2026). https://pith.science/paper/7LDF6DMH

@misc{pith2026250702082,
  author       = {Pith},
  title        = {Pith review of: Adjusting Higher Chern-Simons Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7LDF6DMH}},
  note         = {Machine review of arXiv:2507.02082}
}
read the original abstract

A fundamental problem in formulating higher Chern-Simons theories is the construction of a consistent higher gauge theory that circumvents the fake-flatness constraint. Here, we propose a solution to this problem using adjusted higher connections. In particular, we shall demonstrate that there is an obstruction to constructing such action functionals since, generically, adjusted higher gauge algebras do not admit an inner product. To overcome this obstruction, we introduce half-adjusted higher Chern-Simons theories. These theories have both well-defined underlying kinematic data as well as the expected properties of a higher generalisation of Chern-Simons theory. We develop the general construction of these theories in arbitrary dimensions and provide explicit details for the four-dimensional case. We also present the complete differential cohomological framework for principal 2-bundles with half-adjusted connections. Finally, we discuss an alternative approach introducing additional trivial symmetries.

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Reference graph

Works this paper leans on

56 extracted references · 27 canonical work pages

  1. [1]

    Chern and J

    S.-S. Chern and J. Simons,Characteristic forms and geometric invariants,Ann. Math. 99 (1974) 48

    work page 1974

  2. [2]

    Witten,Quantum field theory and the Jones polynomial,Commun

    E. Witten,Quantum field theory and the Jones polynomial,Commun. Math. Phys.121 (1989) 351

    work page 1989

  3. [3]

    Bagger and N

    J. Bagger and N. D. Lambert,Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D77 (2008) 065008 [0711.0955 [hep-th] ]

    arXiv 2008

  4. [4]

    Gustavsson, Algebraic structures on parallel M2-branes,Nucl

    A. Gustavsson, Algebraic structures on parallel M2-branes,Nucl. Phys. B 811 (2009) 66 [0709.1260 [hep-th] ]

    arXiv 2009

  5. [5]

    Ben-Shahar and H

    M. Ben-Shahar and H. Johansson,Off-shell color–kinematics duality for Chern–Simons,JHEP 2208 (2022) 035 [2112.11452 [hep-th] ]

    arXiv 2022

  6. [6]

    Borsten, B

    L. Borsten, B. Jurčo, H. Kim, T. Macrelli, C. Saemann, and M. Wolf,Kinematic Lie algebras from twistor spaces,Phys. Rev. Lett.131 (2023) 041603 [2211.13261 [hep-th] ]

    arXiv 2023

  7. [7]

    Witten, Chern-Simons gauge theory as a string theory, Prog

    E. Witten, Chern-Simons gauge theory as a string theory, Prog. Math. 133 (1995) 637 [hep-th/9207094]

    arXiv 1995

  8. [8]

    Witten,Perturbative gauge theory as a string theory in twistor space,Commun

    E. Witten,Perturbative gauge theory as a string theory in twistor space,Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171]

    arXiv 2004

Show all 56 references
  1. [9]

    Cederwall, Pure spinor superfields – an overview,Springer Proc

    M. Cederwall, Pure spinor superfields – an overview,Springer Proc. Phys. 153 (2014) 61 [1307.1762 [hep-th] ]

    2014 arXiv

  2. [10]

    Costello,Supersymmetric gauge theory and the Yangian,1303.2632 [hep-th]

    K. Costello,Supersymmetric gauge theory and the Yangian,1303.2632 [hep-th]

    arXiv

  3. [11]

    Costello, E

    K. Costello, E. Witten, and M. Yamazaki,Gauge theory and integrability, I,ICCM Not. 6 (2018) 46 [1709.09993 [hep-th] ]

    2018 arXiv

  4. [12]

    K. J. Costello, E. Witten, and M. Yamazaki,Gauge theory and integrability, II,ICCM Not. 6 (2018) 120 [1802.01579 [hep-th] ]

    2018 arXiv

  5. [13]

    Costello and M

    K. Costello and M. Yamazaki,Gauge theory and integrability, III,1908.02289 [hep-th]

    1908 arXiv

  6. [14]

    Alexandrov, M

    M. Alexandrov, M. Kontsevich, A. Schwarz, and O. Zaboronsky,The geometry of the mas- ter equation and topological quantum field theory,Int. J. Mod. Phys. A 12 (1997) 1405 [hep-th/9502010]

    1997 arXiv

  7. [15]

    Girelli and H

    F. Girelli and H. Pfeiffer,Higher gauge theory – differential versus integral formulation,J. Math. Phys. 45 (2004) 3949 [hep-th/0309173]

    2004 arXiv

  8. [16]

    Girelli, H

    F. Girelli, H. Pfeiffer, and E. M. Popescu,Topological higher gauge theory - from BF to BFCG theory, J. Math. Phys.49 (2008) 032503 [0708.3051 [hep-th] ]

    2008 arXiv

  9. [17]

    J. F. Martins and A. Mikovic,Lie crossed modules and gauge-invariant actions for 2-BF theories, Adv. Theor. Math. Phys.15 (2011) 1059 [1006.0903 [hep-th] ]

    2011 arXiv

  10. [18]

    Radenkovic and M

    T. Radenkovic and M. Vojinovic,Higher gauge theories based on 3-groups,JHEP 1910 (2019) 222 [1904.07566 [hep-th] ]

    2019 arXiv

  11. [19]

    Stipsic and M

    P. Stipsic and M. Vojinovic,Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity,2506.17722 [gr-qc]

  12. [20]

    Fiorenza, C

    D. Fiorenza, C. L. Rogers, and U. Schreiber,A higher Chern–Weil derivation of AKSZσ-models, Int. J. Geom. Meth. Mod. Phys.10 (2013) 1250078 [1108.4378 [math-ph] ]. 45

    2013 arXiv

  13. [21]

    Antoniadis and G

    I. Antoniadis and G. Savvidy,Extension of Chern–Simons forms and new gauge anomalies, Int. J. Mod. Phys. A29 (2014) 1450027 [1304.4398 [hep-th] ]

    2014 arXiv

  14. [22]

    D. Song, M. Wu, K. Wu, and J. Yang,Higher Chern–Simons based on (2-)crossed modules, JHEP 2307 (2023) 207 [2212.04667 [math-ph] ]

    2023 arXiv

  15. [23]

    D. H. Song, K. Wu, and J. Yang,Higher Chern–Simons-Antoniadis-Savvidy forms based on crossed modules,Phys. Lett. B848 (2024) 138374 [2306.08930 [math-ph] ]

    2024 arXiv

  16. [24]

    Soncini and R

    E. Soncini and R. Zucchini,4-d semistrict higher Chern–Simons theory I,JHEP 1410 (2014) 79 [1406.2197 [hep-th] ]

    2014 arXiv

  17. [25]

    Zucchini,A Lie based 4-dimensional higher Chern–Simons theory,J

    R. Zucchini,A Lie based 4-dimensional higher Chern–Simons theory,J. Math. Phys.57 (2016) 052301 [1512.05977 [hep-th] ]

    2016 arXiv

  18. [26]

    Zucchini,Wilson surfaces for surface knots,1903.02853 [hep-th]

    R. Zucchini,Wilson surfaces for surface knots,1903.02853 [hep-th]

    1903 arXiv

  19. [27]

    Zucchini,4-d Chern–Simons theory: Higher gauge symmetry and holographic aspects,JHEP 2106 (2021) 025 [2101.10646 [hep-th] ]

    R. Zucchini,4-d Chern–Simons theory: Higher gauge symmetry and holographic aspects,JHEP 2106 (2021) 025 [2101.10646 [hep-th] ]

    2021 arXiv

  20. [28]

    Chen,Combinatorial quantization of 4d 2-Chern–Simons theory II: Quantum invariants of higher ribbons inD4, 2506.05785 [math-ph]

    H. Chen,Combinatorial quantization of 4d 2-Chern–Simons theory II: Quantum invariants of higher ribbons inD4, 2506.05785 [math-ph]

  21. [29]

    Chen,Combinatorial quantization of 4d 2-Chern–Simons theory I: the Hopf category of higher-graph states, 2501.06486 [math-ph]

    H. Chen,Combinatorial quantization of 4d 2-Chern–Simons theory I: the Hopf category of higher-graph states, 2501.06486 [math-ph]

  22. [30]

    Schenkel and B

    A. Schenkel and B. Vicedo,5d 2-Chern–Simons theory and 3d integrable field theories,Commun. Math. Phys. 405 (2024) 293 [2405.08083 [hep-th] ]

    2024 arXiv

  23. [31]

    Chen and J

    H. Chen and J. Liniado,Higher gauge theory and integrability,Phys. Rev. D110 (2024) 086017 [2405.18625 [hep-th] ]

    2024 arXiv

  24. [32]

    Encyclopedia of Mathematical Physics (Second Edition),

    L. Borsten, M. Jalali Farahani, B. Jurčo, H. Kim, J. Narozny, D. Rist, C. Saemann, and M. Wolf,Higher gauge theory,in: “Encyclopedia of Mathematical Physics (Second Edition),” Vol.4, pp.159-185, Elsevier [doi] [2401.05275 [hep-th] ]

    arXiv

  25. [33]

    Quantum Field Theory,

    H. Sati, U. Schreiber, and J. Stasheff,L8-algebra connections and applications to String- and Chern–Simons n-transport,in: “Quantum Field Theory,” eds. B. Fauser, J. Tolksdorf and E. Zeidler, p. 303, Birkhäuser 2009 [doi] [0801.3480 [math.DG] ]

    2009 arXiv

  26. [34]

    Saemann and L

    C. Saemann and L. Schmidt,Towards an M5-brane model II: Metric string structures,Fortschr. Phys. 68 (2020) 2000051 [1908.08086 [hep-th] ]

    2020 arXiv

  27. [35]

    Kim and C

    H. Kim and C. Saemann,Adjusted parallel transport for higher gauge theories,J. Phys. A52 (2020) 445206 [1911.06390 [hep-th] ]

    2020 arXiv

  28. [36]

    D. Rist, C. Saemann, and M. Wolf,Explicit non-Abelian gerbes with connections,2203.00092 [hep-th]

  29. [37]

    Fischer, M

    S.-R. Fischer, M. Jalali Farahani, H. Kim, and C. Saemann,Adjusted connections I: Differential cocycles for principal groupoid bundles with connection,2406.16755 [math.DG]

    arXiv

  30. [38]

    Jurčo, L

    B. Jurčo, L. Raspollini, C. Saemann, and M. Wolf,L8-algebras of classical field theories and the Batalin–Vilkovisky formalism,Fortsch. Phys.67 (2019) 1900025 [1809.09899 [hep-th] ]

    2019 arXiv

  31. [39]

    Higher Structures in M-Theory,

    B. Jurčo, T. Macrelli, L. Raspollini, C. Saemann, and M. Wolf,L8-algebras, the BV formalism, and classical fields,in: “Higher Structures in M-Theory,” proceedings of the LMS/EPSRC Durham Symposium, 12–18 August 2018 [doi] [1903.02887 [hep-th] ]. 46

    2018 arXiv

  32. [40]

    J. C. Baez, D. Stevenson, A. S. Crans, and U. Schreiber,From loop groups to 2-groups,Homol. Homot. Appl. 9 (2007) 101 [math.QA/0504123]

    2007

  33. [41]

    Saemann and L

    C. Saemann and L. Schmidt,Towards an M5-brane model I: A 6d superconformal field theory, J. Math. Phys.59 (2018) 043502 [1712.06623 [hep-th] ]

    2018 arXiv

  34. [42]

    D. Rist, C. Saemann, and M. van der Worp,Towards an M5-brane model III: Self-duality from additional trivial fields,JHEP 2106 (2021) 036 [2012.09253 [hep-th] ]

    2021 arXiv

  35. [43]

    Kadeishvili,Algebraic structure in the homology of anA8-algebra, Soobshch

    T. Kadeishvili,Algebraic structure in the homology of anA8-algebra, Soobshch. Akad. Nauk. Gruz. SSR 108 (1982) 249

    1982

  36. [44]

    Kajiura,Noncommutative homotopy algebras associated with open strings,Rev

    H. Kajiura,Noncommutative homotopy algebras associated with open strings,Rev. Math. Phys. 19 (2007) 1 [math.QA/0306332]

    2007

  37. [45]

    Borsten, H

    L. Borsten, H. Kim, and C. Saemann,EL8-algebras, generalized geometry, and tensor hier- archies, 2106.00108 [hep-th]

  38. [46]

    Gagliardo, C

    G. Gagliardo, C. Saemann, and R. Tellez-Dominguez, Principal 3-bundles with adjusted connections, 2505.13368 [math-ph]

  39. [47]

    Bergshoeff, M

    E. Bergshoeff, M. de Roo, B. de Wit, and P. van Nieuwenhuizen,Ten-dimensional Maxwell– Einstein supergravity, its currents, and the issue of its auxiliary fields,Nucl. Phys. B 195 (1982) 97

    1982

  40. [48]

    G. F. Chapline and N. S. Manton,Unification of Yang–Mills theory and supergravity in ten dimensions, Phys. Lett. B120 (1983) 105

    1983

  41. [49]

    J. C. Baez and A. D. Lauda,Higher-dimensional algebra V: 2-groups,Th. App. Cat.12 (2004) 423 [math.QA/0307200]

    2004

  42. [50]

    Kim and C

    H. Kim and C. Saemann,Non-geometric T-duality as higher groupoid bundles with connections, 2204.01783 [hep-th]

    arXiv

  43. [51]

    Henneaux and C

    M. Henneaux and C. Teitelboim,Quantization of gauge systems,Princeton University Press, 1992 [doi]

    1992

  44. [52]

    Samtleben, E

    H. Samtleben, E. Sezgin, and R. Wimmer,(1,0) superconformal models in six dimensions, JHEP 1112 (2011) 062 [1108.4060 [hep-th] ]

    2011 arXiv

  45. [53]

    Samtleben, E

    H. Samtleben, E. Sezgin, and R. Wimmer,Six-dimensional superconformal couplings of non- abelian tensor and hypermultiplets,JHEP 1303 (2013) 068 [1212.5199 [hep-th] ]

    2013 arXiv

  46. [54]

    E. A. Bergshoeff and M. de Roo,The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B328 (1989) 439

    1989

  47. [55]

    Samtleben,Lectures on gauged supergravity and flux compactifications,Class

    H. Samtleben,Lectures on gauged supergravity and flux compactifications,Class. Quant. Grav. 25 (2008) 214002 [0808.4076 [hep-th] ]

    2008 arXiv

  48. [56]

    Fiorenza, H

    D. Fiorenza, H. Sati, and U. Schreiber,Multiple M5-branes, string 2-connections, and 7d nona- belian Chern–Simons theory,Adv. Theor. Math. Phys.18 (2014) 229 [1201.5277 [hep-th] ]. 47

    2014 arXiv

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