{"total":19,"items":[{"citing_arxiv_id":"2607.08583","ref_index":52,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Holographic Theory of Mixed-Dimensional Statistics and Conservation-Encoding Hopping-Operator Algebras","primary_cat":"cond-mat.str-el","submitted_at":"2026-07-09T15:18:48+00:00","verdict":"CONDITIONAL","verdict_confidence":"HIGH","novelty_score":6.5,"formal_verification":"none","one_line_summary":"Statistics of G-conserved invertible mixed-dimensional excitations in d-space are classified by H^{d+2}(BG; R/Z) and realized as boundary excitations of an ω-twisted higher-group gauge theory.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2607.07786","ref_index":26,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging","primary_cat":"hep-th","submitted_at":"2026-07-08T18:00:00+00:00","verdict":"ACCEPT","verdict_confidence":"HIGH","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.03582","ref_index":47,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Fracton Topological Holography","primary_cat":"quant-ph","submitted_at":"2026-06-02T12:50:55+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Introduces FTH as an extension of TH/SymTFT to type-I and type-II fracton orders, demonstrating boundary switches and dualities for X-cube and Haah's code via stabilizer formalism.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.31601","ref_index":23,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Twin Phases: Intrinsic Deconfined Quantum Criticality","primary_cat":"cond-mat.str-el","submitted_at":"2026-05-29T17:59:38+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.31602","ref_index":24,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Twin Algebras: Condensable Algebras beyond Anyons","primary_cat":"cond-mat.str-el","submitted_at":"2026-05-29T17:59:38+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.28485","ref_index":11,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries","primary_cat":"hep-th","submitted_at":"2026-05-27T13:42:18+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A quantum mechanical framework is given for Hilbert and defect spaces of line operators in BF+kCS TQFT, with line operator action realized by convolution kernels and matches to Verlinde and semiclassical Hopf-link data.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.07734","ref_index":79,"ref_count":9,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries","primary_cat":"hep-th","submitted_at":"2026-05-08T13:41:03+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":6.0,"formal_verification":"none","one_line_summary":"For dual massive RG flows, the gapped-phase module is spanned by smeared Ishibashi states and cannot be reduced to the boundary-critical Cardy-state module, even in the simplest tricritical-Ising to Ising flow.","context_count":3,"top_context_role":"background","top_context_polarity":"background","context_text":"Wen, and H. Zheng,Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers,2015. https://arxiv.org/abs/1502.01690. [78] W. Ji and X.-G. Wen,Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions,Phys. Rev. Res.2(2020) 033417, arXiv:1912.13492 [cond-mat.str-el]. [79] A. Chatterjee and X.-G. Wen,Symmetry as a shadow of topological order and a derivation of topological holographic principle,Phys. Rev. B107(2023) 155136, arXiv:2203.03596 [cond-mat.str-el]. [80] F. Apruzzi, F. Bonetti, I. García Etxebarria, S. S. Hosseini, and S. Schafer-Nameki,Symmetry TFTs from String Theory,Commun. Math. Phys.402(2023) 895-949, arXiv:2112."},{"citing_arxiv_id":"2604.25821","ref_index":4,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Categorical Symmetries via Operator Algebras","primary_cat":"hep-th","submitted_at":"2026-04-28T16:30:42+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra, enabling braiding computations in the 3D SymTFT.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"A bundle gerbeGover a smooth manifoldMis given by the following data: 1. a surjective submersionφ:Y→M; 2. aU(1)-principle bundle L→Y× M Y ,(D.1) over the fiber product;22 3. an isomorphism ofU(1)-bundles onY [3] :=Y× M Y× M Y, ρ:L 12 ⊗L 23 →L 13 ,(D.2) whereL ij is the pullback ofLto the(i, j)-th factor ofY [3]; 4. the isomorphism is associative overY[4] :=Y× M Y× M Y× M Y, namely, ρ1,3,4 ◦(ρ 1,2,3 ⊗id) =ρ 1,2,4 ◦(id⊗ρ 2,3,4).(D.3) For our purpose, we take the base manifoldMto be the Lie groupG. To incorporate the group multiplication structurem:G×G→Gand associativity, we require the bundle gerbe to host the corresponding structures, rendering the bundle gerbe multiplicative. Definition D.2(Multiplicative bundle gerbe)."},{"citing_arxiv_id":"2602.11696","ref_index":38,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Symmetry Spans and Enforced Gaplessness","primary_cat":"cond-mat.str-el","submitted_at":"2026-02-12T08:22:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"[36] Wenjie Ji and Xiao-Gang Wen, \"Categorical symme- try and noninvertible anomaly in symmetry-breaking and topological phase transitions,\" Phys. Rev. Res.2, 033417 (2020), arXiv:1912.13492 [cond-mat.str-el]. [37] Michael Levin, \"Constraints on order and disorder pa- rameters in quantum spin chains,\" Commun. Math. Phys.378, 1081-1106 (2020), arXiv:1903.09028 [cond- mat.str-el]. [38] Yui Hayashi and Yuya Tanizaki, \"Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly,\" JHEP08, 036 (2022), arXiv:2204.07440 [hep-th]. [39] Avner Karasik, \"On anomalies and gauging of U(1) non- invertible symmetries in 4d QED,\" SciPost Phys.15, 002 (2023), arXiv:2211.05802 [hep-th]. [40] Anuj Apte, Clay Cordova, and Ho Tat Lam, \"Obstruc-"},{"citing_arxiv_id":"2602.03926","ref_index":9,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"The Line, the Strip and the Duality Defect","primary_cat":"hep-th","submitted_at":"2026-02-03T19:00:00+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2508.13961","ref_index":26,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Fusion Rules of Mobility","primary_cat":"quant-ph","submitted_at":"2025-08-19T15:53:45+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"In Z2 topological order enriched by subsystem symmetries, mobility classes obey multi-channel fusion algebras including Fibonacci rules, tensor products thereof, and lineon period transmutation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2504.11449","ref_index":9,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"SymTFT construction of gapless exotic-foliated dual models","primary_cat":"cond-mat.str-el","submitted_at":"2025-04-15T17:57:58+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY plaquette and XYZ cube models.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2405.15648","ref_index":30,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Self-$G$-ality in 1+1 dimensions","primary_cat":"cond-mat.str-el","submitted_at":"2024-05-24T15:40:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2405.05964","ref_index":36,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"paper_title":"Lattice Models for Phases and Transitions with Non-Invertible Symmetries","primary_cat":"cond-mat.str-el","submitted_at":"2024-05-09T17:59:00+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2308.00747","ref_index":204,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"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":"Having discussed the conserved operatorD of the transverse-field Ising model, we now briefly discuss the corresponding topological defect. The Ising Hamiltonian twisted by this non-invertible defect is given by [206, 156, 23-25, 155] HD = − NX j=2 (Xj + Zj−1Zj) − ZN X1 . (3.67) 24The Z2 × Z2 symmetry generated by (−1)F andeη in eH is the \"categorical symmetry\" of [204]. However, the system with the Hamiltonian eH on the 2N +1-dimensional Hilbert space is not a local 1+1d system, but the boundary of a 2+1d system. See [205] for the latter perspective. 25Comparing with the convention in (3.34) in the continuum, here we flip the(−1)F eigenvalues in the RR Hilbert space by stacking the Majorana CFT with an Arf invariant."},{"citing_arxiv_id":"2305.18296","ref_index":116,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"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":"The most pressing question is whether we can derive genuinely new prop- erties of QFTs from non-invertible symmetries. Some interesting applications have been put forward in the context of the Standard Model, but they are still not quite as compelling as we would like them to be (e.g. the constraints on pion-decays can be derived without the use of non-invertible symmetries), see [18, 24, 39, 44, 57, 116, 117] for a selection of such applications. In 2d many powerful applications of fusion category symmetries are known [7,9] and one im- portant advance would be to derive similarly powerful statements in higher-dimensions. One obvious application is in the context of confinement/deconfinement, with some results in [28]. Symmetries in String Theory/Holography ."},{"citing_arxiv_id":"2205.09545","ref_index":129,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"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":"More recently, infinitely many non-invertible global symmetries were identified in the Standard Model and axion models from ABJ anomalies [8, 9]. Non-invertible defects have also found applications in quantum gravity in the context of the complete- ness hypothesis [114-118]. They have also been realized on the lattice [119-125,108,126-128], sometimes under the name of \"algebraic higher symmetry\" [129, 45]. 2.5 Subsystem Symmetries and Fractons A novel kind of global symmetry, known as subsystem global symmetry , has featured prominently in many condensed matter systems, including the gapless model of [130] and many gapped fracton models 27 The search for hidden symmetry has a long history in these theories. For instance, in rational CFTs any primary operator"},{"citing_arxiv_id":"2204.02407","ref_index":31,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"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":"non-invertible if there does not exist an inverse topological operator U −1 such that under parallel fusion, U × U −1 = U −1 × U = 1. Non-invertible symmetries were discussed extensively in the context of 1+1d CFT [5-7] (see also [8-10] and more recently [11-19]). They have also been realized on the lattice [20-30] and are sometimes discussed under the name of algebraic higher symmetries [31, 32]. The simplest example is the Kramers-Wannier duality, generated by a topological line in the 1+1d Ising model [33-35]. Recently, non-invertible defects have been found in many familiar gauge theories in 2+1d and 3+1d, both in the continuum [36,37] and on the lattice [38,27,36]. It has been advocated that these non-invertible topological operators should be viewed"},{"citing_arxiv_id":"2111.01139","ref_index":50,"ref_count":1,"confidence":0.9,"is_internal_anchor":false,"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}