{"total":18,"items":[{"citing_arxiv_id":"2606.26004","ref_index":86,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Non-invertible symmetries in the axiverse, and the imaginary wormholes","primary_cat":"hep-th","submitted_at":"2026-06-24T16:21:20+00:00","verdict":"CONDITIONAL","verdict_confidence":"HIGH","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.05543","ref_index":106,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Notes on (-2)-form symmetries","primary_cat":"hep-th","submitted_at":"2026-06-04T00:58:08+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":6.0,"formal_verification":"none","one_line_summary":"(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.16482","ref_index":80,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"When Symmetries Twist: Anomaly Inflow on Monodromy Defects","primary_cat":"hep-th","submitted_at":"2026-05-15T18:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"σH −c − = 0 mod 8,for invertible states.(5.11) This is to be contrasted with the Spin picture, in which the Spin(n) 1 theory lets us always offset the chiral central charge by half units. Consider nowq= 1 which implies thatk= 1, ekg = 0, the strategy is valid in general. For rational ν=p/Nwe start by matching the Hall conductance by a minimalZ N TQFTA N,p [80]. See Appendix D for details about these theories and their compatibility with the Spin c structure. This is done by symmetry fractionalization: the minimal theory carries a 1-form symmetry anomaly: Ωm,N(B) = πm N P(B),(5.12) wherePis the Pontryagin square operation. 10 In our conventions the generating lineLhas spin θL = exp \u0012 πip N \u0013 ,(5.13) and chargepunder the one-form symmetry."},{"citing_arxiv_id":"2605.12601","ref_index":3,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions","primary_cat":"cond-mat.str-el","submitted_at":"2026-05-12T18:00:04+00:00","verdict":null,"verdict_confidence":null,"novelty_score":null,"formal_verification":null,"one_line_summary":null,"context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"2 -theory with dual symmetry defects that would need to be projected out. References [1] D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett,Generalized global symmetries, Journal of High Energy Physics2015(2), 1 (2015), doi:https://doi.org/10.1007/JHEP02(2015)172. [2] E. Sharpe,Notes on generalized global symmetries in QFT, Fortsch. Phys.63, 659 (2015), doi:10.1002/prop.201500048,1508.04770. [3] P.-S. Hsin, H. T. Lam and N. Seiberg,Comments on One-Form Global Sym- metries and Their Gauging in 3d and 4d, SciPost Phys.6(3), 039 (2019), doi:10.21468/SciPostPhys.6.3.039,1812.04716. [4] C. C' ordova, T. T. Dumitrescu and K. Intriligator,Exploring 2-Group Global Sym- metries, JHEP02, 184 (2019), doi:10.1007/JHEP02(2019)184,1802.04790. [5] E. Lake,Higher-form symmetries and spontaneous symmetry breaking(2018),1802."},{"citing_arxiv_id":"2605.12594","ref_index":30,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"String probes, simple currents, and the no global symmetries conjecture","primary_cat":"hep-th","submitted_at":"2026-05-12T18:00:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Chiral simple current extensions on the worldsheet reproduce and generalize obstructions to gauging center one-form symmetries in 6d and 8d string compactifications while clarifying BPS particle requirements upon circle reduction.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"or F-theory, these classes of strings can be realized by wrapping respectively M5 or D3 branes on suitable holomorphic cycles in the internal geometry, and their low energy behavior is again described by two-dimensional theories with conformal symmetry. Al- though in this paper we focus exclusively on examples ind≥6 with at least eight supercharges, it is worth mentioning that faithful string probes (possibly generalized 3See [30] for related remarks. - 7 - in a suitable way) may be a useful concept in a broader setting. Here we will content ourselves with mentioning a few possibilities. First of all, five-dimensional minimal su- pergravity theories possess supergravity strings which are described by (0,4) CFTs in the infrared and have been studied in [8, 32]. At a generic point on the Coulomb branch"},{"citing_arxiv_id":"2605.06287","ref_index":37,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Half-Spacetime Gauging of 2-Group Symmetry in 3d","primary_cat":"hep-th","submitted_at":"2026-05-07T13:56:33+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Constructs non-invertible duality defects in (2+1)d QFTs from half-spacetime gauging of 2-group symmetries and derives explicit fusion rules with examples in U(1)^3 gauge theories.","context_count":1,"top_context_role":"other","top_context_polarity":"unclear","context_text":"Teleman,Topological dualities in the Ising model,Geom. Topol.26(2022) 1907-1984, [1806.00008]. - 35 - [35] Y. Choi, Y. Sanghavi, S.-H. Shao and Y. Zheng,Non-invertible and higher-form symmetries in 2+1d lattice gauge theories,2405.13105. [36] W. Cui, B. Haghighat and L. Ruggeri,Non-invertible surface defects in 2+1d QFTs from half spacetime gauging,JHEP11(2024) 159, [2406.09261]. [37] P.-S. Hsin, H. T. Lam and N. Seiberg,Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d,SciPost Phys.6(2019) 039, [1812.04716]. [38] K. Roumpedakis, S. Seifnashri and S.-H. Shao,Higher Gauging and Non-invertible Condensation Defects,2204.02407. [39] S. Seifnashri and S.-H. Shao,Cluster state as a non-invertible symmetry protected topological"},{"citing_arxiv_id":"2604.18702","ref_index":28,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Confinement in a finite duality cascade","primary_cat":"hep-th","submitted_at":"2026-04-20T18:02:02+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"Holographic consistency checks confirm confinement (area law), domain-wall dynamics matching YM-CS theory, and absence of stable axionic strings in a D3/O7-conifold gauge/gravity dual.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Note that one could turn the reasoning around and use the knowledge of the SPT phase difference between the two sides of the domain wall to determine the theory that has the right anomaly to absorb it. However, such theory is not unique. In the present case, one would just determine that the domain wall theory has to have a topological subsector coupling to the bulk 1-form symmetry given by theA2,N theory of [28]. Indeed,SUp2qN CS has such a subsector, but is an obviously richer theory. For instance, forNeven one would actually think that there is no need for a non-trivial domain wall theory since the SPT does not jump across the domain wall. On the other handSUp2qN CS is a non-trivial TQFT also forNeven. Supersymmetry is more powerful in determining the theory living on the domain wall, which in the present"},{"citing_arxiv_id":"2602.09105","ref_index":102,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Generalized Families of QFTs","primary_cat":"hep-th","submitted_at":"2026-02-09T19:00:17+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"whereF 2 is the field strength of the dynamicalU(1) g gauge field. Because of the anomalous conservation equation, the naive symmetry defect operatore iα H ∗j5 is not topological. For α= 2πqwithq∈Q/Z, we can construct a topological operator Dq(Σ) =e 2πiq H Σ ∗j5 AN,p \u0014 Σ; F2 2π \u0015 ,(2.8) whereq=p/Nfor gcd(p, N) = 1 andA N,p[Σ;B 2] is the minimal 3dZ N TQFT on Σ of [102]. The TQFTA N,p\u0002 Σ; F2 2π \u0003 gauges aZ N subgroup of theU(1) (1) m 1-form magnetic symmetry on Σ with a torsion term. Another construction of theA N,p[Σ;B 2] TQFT is in terms of the half-space gauging construction of [69, 72] which couples the QFT to a TQFT on one component of spacetime divided by Σ: AN,p[Σ;B 2] =⇒S T QF T[B2] = Z σ+ iN 2π dc1 ∧b 2 +ib 2 ∧B 2 + ikN"},{"citing_arxiv_id":"2511.15783","ref_index":24,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates","primary_cat":"cond-mat.str-el","submitted_at":"2025-11-19T19:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Automorphisms of gauge groups extend to higher or non-invertible symmetries in topological gauge theories and enable transversal non-Clifford gates in 2+1d Z_N qudit Clifford stabilizer models for N greater than or equal to 3.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2506.08178","ref_index":8,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging","primary_cat":"math.QA","submitted_at":"2025-06-09T19:42:49+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"The paper proves that 2-group symmetries in 3D defect TQFTs from G-crossed braided fusion categories have no gauging obstructions and that gauging the 0-form G-symmetry on the neutral component produces the equivariantisation, with a reciprocal relation when G is commutative.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2408.01490","ref_index":51,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT","primary_cat":"hep-th","submitted_at":"2024-08-02T18:00:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2312.16317","ref_index":19,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Non-Invertible Anyon Condensation and Level-Rank Dualities","primary_cat":"hep-th","submitted_at":"2023-12-26T19:53:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2308.00747","ref_index":240,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries","primary_cat":"hep-th","submitted_at":"2023-08-01T18:00:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":3.0,"formal_verification":"none","one_line_summary":"A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"We obtain a condensation defect Cn for each Zn subgroup of ZN, with n|N. Their fusion rule is [67] Cn × Cn′ = (Zgcd(n,n′,kℓ)) C gcd(n,n′,kℓ)nn′ gcd(n,n′)2 , ℓ = N lcm(n, n′) . (5.7) In particular, C1 is the trivial surface defect. When k = 1, this reduces to the algebra in [214]. Mathematically, the topological lineη, the condensation surfaceC, and their composites form a fusion 2-category [240]. See also [241,242] for the mathematical formulation of the condensation surfaces discussed above. See [116] for 2+1d lattice models realizing a general fusion 2-category. See also [243-246, 211, 247, 248] for the gauging of these topological surfaces. 5.3 Examples in 2+1d TQFT In this subsection we discuss some examples of condensation defects in 2+1d TQFT."},{"citing_arxiv_id":"2307.07547","ref_index":90,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Lectures on Generalized Symmetries","primary_cat":"hep-th","submitted_at":"2023-07-14T18:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":1.0,"formal_verification":"none","one_line_summary":"Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"and is referred to as thePontryagin dual groupof G(p). Phrased in this language, the charge carried by a (irreducible)p-dimensional operator under ap-form symmetry groupG(p) is an element of the Pontryagin dual groupˆG(p). Let us discuss some examples: • ForG(p) =U(1), we haveˆG(p) = Z, namely the group formed by integers under addition. If we represent the elements ofG(p) as g =eiα, α ∈[0, 2π) (2.67) 19 the possible homomorphisms are ϕ(g) =gq =eiqα∈U(1), q ∈Z. (2.68) • ForG(p) = ZN, we have ˆG(p) = ZN, namely the group formed by integers moduloN under addition. If we represent the elements ofG(p) as g =e 2πiα N , α ∈{0, 1,···N−1}, (2.69) the possible homomorphisms are ϕ(g) =gq =e 2πiqα N , q ∈{0, 1,···N−1}. (2.70) • Generalizing the previous example, ifG(p) is afinite abelian group, then we have ˆG(p)∼=G(p) (2.71) This can actually be derived as a consequence of the previous example. For a finite abelian group, we have G(p)∼= n∏ i=1 ZNi, N i∈N (2.72) and consequently ˆG(p)∼= n∏ i=1 ˆZNi ∼= n∏ i=1 ZNi (2.73) Double Pontryagin Duality An important property of Pontryagin duals that we will use later is that taking the Pontryagin dual twice is equivalent to not taking the Pontryagin dual at all. More precisely, there exists a canonical isomorphism ˆˆG(p)∼=G(p) (2.74) for any groupG(p). Indeed, an elementg∈G(p) defines a homomorphism hg : ˆG(p)→U(1) (2.75) taking the form hg(ϕ) =ϕ(g)∈U(1), ϕ ∈ˆG(p). (2.76) 20 Special Case: U(1) p-Form Symmetry. Generalizing example 2.1, the continuity equa- tion for the Noether current of aU(1) p-form symmetry is modified in the presence of a p-dimensional operator ofO(Mp) of chargeq∈Z; O(Mp)djd−p−1 =qδd−p(Mp)O(Mp), (2.77) where δd−p(Mp) is the (d−p)-form associated to delta function onMp. Using this fact and following steps similar to those in derivation (2.37), we can compute the linking action (2.63) ofp-form symmetry withO(Mp) to be Ug ( Sd−p−1 ) O(Mp) = exp (iqα)O(Mp). (2.78) Example 2.3: Higher-Form Charges in the Maxwel"},{"citing_arxiv_id":"2305.18296","ref_index":105,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"ICTP Lectures on (Non-)Invertible Generalized Symmetries","primary_cat":"hep-th","submitted_at":"2023-05-29T17:59:50+00:00","verdict":"ACCEPT","verdict_confidence":"MODERATE","novelty_score":2.0,"formal_verification":"none","one_line_summary":"Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"This effect is called symmetry fractionalization, which means that a symmetry - here G(0) - of the theory gets enlarged, when restricted to an operator Oq. The larger group, G(0),frac arises because the defect itself may have topological lines that are not arising from restrictions of topological defects of the bulk (they are localized symmetries). In the context of condensed matter physics this was already observed in [105]. The distinction between induced and localized symmetries is illustrated in figure 14: • Localized: topological defects that are localized on the operator O2 • Induced: topological defects that arise as intersections of O2 with bulk 0-form symmetry generators D(g) d−1. A 2-charge O2 for a 0-form symmetry G(0) that admits such symmetry fractionalization"},{"citing_arxiv_id":"2205.09545","ref_index":28,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond","primary_cat":"hep-th","submitted_at":"2022-05-19T13:15:29+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Sharpe, Notes on generalized global symmetries in QFT, Fortsch. Phys. 63 (2015) 659-682, [arXiv:1508.04770]. [26] D. Gaiotto, A. Kapustin, Z. Komargodski, and N. Seiberg, Theta, Time Reversal, and Temperature, JHEP 05 (2017) 091, [arXiv:1703.00501]. [27] D. M. Hofman and N. Iqbal, Generalized global symmetries and holography, SciPost Phys. 4 (2018), no. 1 005, [arXiv:1707.08577]. [28] P.-S. Hsin, H. T. Lam, and N. Seiberg, Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d, SciPost Phys. 6 (2019), no. 3 039, [arXiv:1812.04716]. [29] P.-S. Hsin and S.-H. Shao, Lorentz Symmetry Fractionalization and Dualities in (2+1)d, SciPost Phys. 8 (2020) 018, [arXiv:1909.07383]. [30] D. R. Morrison, S. Schafer-Nameki, and B."},{"citing_arxiv_id":"2204.02407","ref_index":94,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Higher Gauging and Non-invertible Condensation Defects","primary_cat":"hep-th","submitted_at":"2022-04-05T18:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"the choice of the triangulation, which is equivalent to demanding the braiding of these lines to be trivial. This implies that the topological spins of these lines are all trivial, i.e., they are boson lines. Hence, a 1-form global symmetry is free of 't Hooft anomalies if the braiding of the associated topological lines is trivial [1,92,93]. See [93] (which was based on [94,95]) for 16For more general non-invertible lines, the topological spin is defined as θ(a) = (Ra,¯a 1 )−1 where ¯a is the orientation-reversal of a. 17Because of this relation, B(a, b) is sometimes referred to as the double-braiding phase (or monodromy phase), and R as the braiding. We will loosely refer to both of them as braiding. 12 Figure 4: Gauging a q-form symmetry on a codimension-p manifold is equivalent to inserting"},{"citing_arxiv_id":"2111.01139","ref_index":68,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Non-Invertible Duality Defects in 3+1 Dimensions","primary_cat":"hep-th","submitted_at":"2021-11-01T18:00:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"MODERATE","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and lattice models.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}