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Article
Physics, Multidisciplinary
Jonathan J. Heckman et al.
Summary: The modern approach to m-form global symmetries in d-dimensional QFT involves specifying dimension d-m-1 topological generalized symmetry operators that link with m-dimensional defect operators. These defects originate from branes wrapped on non-compact cycles in a non-compact geometry X. The generalized symmetry operators associated with these defects arise from magnetic dual branes wrapped on cycles in partial differential X∂X.
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
(2023)
Article
Physics, Multidisciplinary
Lakshya Bhardwaj et al.
Summary: We propose a procedure to capture general non-invertible symmetries of d-dimensional quantum field theories using the data of a higher-category. This procedure captures the local properties of topological defects associated with the symmetries. We also discuss the fusion of topological defects and explain that the phenomenon of dimension-changing fusions can be understood as higher-morphisms of the higher-category describing the symmetry.
Article
Physics, Mathematical
Konstantinos Roumpedakis et al.
Summary: We discuss invertible and non-invertible topological condensation defects arising from gauging a discrete higher-form symmetry on a higher codimensional manifold in spacetime, which we define as higher gauging. The universal fusion rules of the resulting invertible and non-invertible condensation surfaces are determined. In the special case of 2+1d TQFT, every (invertible and non-invertible) 0-form global symmetry, including the Z(2) electromagnetic symmetry of the Z2 gauge theory, is realized from higher gauging. We further compute the fusion rules between the surfaces, the bulk lines, and lines that only live on the surfaces, determining some of the most basic data for the underlying fusion 2-category. We emphasize that the fusion coefficients in these non-invertible fusion rules are generally not numbers, but rather 1+1d TQFTs. Finally, we discuss examples of non-invertible symmetries in non-topological 2+1d QFTs such as the free U(1) Maxwell theory and QED.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Mathematical
Yichul Choi et al.
Summary: We discuss a variety of non-invertible, codimension-one topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These defects include condensation defects from higher gauging of one-form symmetries, labeled by discrete torsion classes, and duality and triality defects from gauging in half of spacetime. The fusion rules between these defects and the one-form symmetry surface defects are determined to be 2+1d TQFTs.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Fabio Apruzzi et al.
Summary: We propose a systematic approach to deriving symmetry generators in holography. We focus on noninvertible symmetries, which have emerged as a new type of symmetry in higher-dimensional quantum field theories. We provide an example in the holographic confinement setup, where the fusion of noninvertible symmetries arises from the Myers effect on D-branes.
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Multidisciplinary
Horacio Casini et al.
Summary: We establish the irreversibility of renormalization group flows on a pointlike defect in a d-dimensional Lorentzian conformal field theory by relating the impurity entropy g to the quantum relative entropy in two equivalent ways. Through a null deformation of the Cauchy surface and a local quench protocol, we show that the positivity and monotonicity of the relative entropy imply a monotonic decrease of g along renormalization group flows, providing a clear information-theoretic meaning for this irreversibility.
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Multidisciplinary
Clay Cordova et al.
Summary: We explain what happens to classical symmetries with Abelian Adler-Bell-Jackiw anomalies. Rather than being completely destroyed, these symmetries survive as noninvertible topological global symmetry defects with world volume anyon degrees of freedom that couple to the bulk through a magnetic 1-form global symmetry. These noninvertible chiral symmetries lead to selection rules on correlation functions, and they appear in well-known models of massless quantum electrodynamics and axion models.
Article
Physics, Particles & Fields
Ying-Hsuan Lin et al.
Summary: This paper investigates the case of a 2d CFT in a fusion category C, where the asymptotic density of states is proportional to (dim ρ)^2 for an irreducible representation ρ of a finite symmetry group G, even when the symmetry can be non-invertible.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Multidisciplinary
Shi Chen et al.
Summary: We find a more sophisticated algebraic structure when solitons of different dimensions coexist in the spectrum of a concrete quantum field theory. By evaluating the hopfion charge of vortex operators, we demonstrate the nonexistence of the hopfion U(1) symmetry. We clarify that what conserves hopfion numbers is a noninvertible symmetry generated by 3D spin topological quantum field theories (TQFTs).
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Particles & Fields
Horacio Casini et al.
Summary: We analyze infinitesimal null deformations for the entanglement entropy, simplifying the proof of the C, F and A-theorems. Then, we study the quantum null energy condition (QNEC) on the light-cone for a CFT. Finally, we combine these tools to prove the irreversibility of renormalization group flows on planar d-dimensional defects in D-dimensional conformal field theories.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Editorial Material
Physics, Particles & Fields
Federico Carta et al.
Summary: We demonstrate the presence of non-invertible symmetries in an infinite family of superconformal Argyres-Douglas theories, which arise from diagonal gauging of the flavor symmetry of D-p(SU(N)) theories and can also be realized from 6d N = (1, 0) compactification on a torus. The (A(2), D-4) theory is the main example in this class and shares the same structures of non-invertible duality and triality defects as N = 4 super Yang-Mills with gauge algebra su(2). We extend this result to infinitely many other Argyres-Douglas theories, including those with one-dimensional conformal manifold and those with a ≠ c and higher-dimensional conformal manifold. Our result is supported by examining certain special cases that can be realized in terms of theories of class S.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Anuj Apte et al.
Summary: In this paper, we study the novel noninvertible duality symmetries encoded by topological defects in 3+1-dimensional quantum systems that are invariant under gauging a one-form symmetry. These symmetries, which are renormalization group invariants, impose constraints on the dynamics. We find that these noninvertible symmetries often prevent the existence of a symmetry-preserving vacuum state with a gapped spectrum. Furthermore, we extend our results to noninvertible symmetries arising from more general gauging operations, including triality symmetries. Along the way, we discover the hidden time-reversal symmetry of duality defects in symmetry-protected topological phases, and these noninvertible symmetries are realized in lattice gauge theories.
Article
Physics, Particles & Fields
Federico Carta et al.
Summary: This study demonstrates the existence of non-invertible symmetries in a family of superconformal Argyres-Douglas theories and examines the specific structures of one theory in detail. Furthermore, this result is extended to other Argyres-Douglas theories.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Physics, Multidisciplinary
Gabriel Cuomo et al.
Summary: This article investigates line defects in conformal field theories and reveals that the flow on these defects is irreversible, accompanied by a decreasing entropy function. The generalization of the g theorem to line defects in arbitrary dimensions is demonstrated through a flow between Wilson loops in four dimensions.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Particles & Fields
Yifan Wang
Summary: This paper studies the universal behaviors of a CFT in the presence of defects, proving that the defect a-anomaly must decrease under unitary defect RG flows and deriving the relation between the defect a- and c-anomalies and the U(1)(R) symmetry anomalies. The methods are illustrated with examples and the potential collider bounds on defect anomalies are discussed.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Multidisciplinary
Masataka Koide et al.
Summary: We explore topological defects in the 4D pure Z(2) lattice gauge theory, including the topological defects of KWW duality and 1-form Z(2) center symmetry, and derive the crossing relations between them.
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS
(2022)
Article
Physics, Mathematical
Theo Johnson-Freyd
Summary: In this paper, we axiomatize the extended operators in topological orders using monoidal Karoubi-complete n-categories that are mildly dualizable and have trivial centres. We show that these n-categorical algebras are Morita-invertible, thus identifying topological orders with anomalous fully-extended TQFTs. We also discuss the classification of topological orders in low spacetime dimensions and confirm and extend previous conjectures and results.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
Justin Kaidi et al.
Summary: We introduce a class of noninvertible topological defects in (3 + 1)D gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)D critical Ising model. Examples include SO(3) Yang-Mills (YM) at theta = pi, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at tau = i. We also introduce an analogous construction in (2 + 1)D, and give a number of examples in Chern-Simons matter theories.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Tzu-Chen Huang et al.
Summary: We numerically studied an anyon chain based on the Haagerup fusion category and found evidence that it leads to a conformal field theory in the long-distance limit, with a central charge of ???2. This is the first example of a conformal field theory with truly exotic generalized symmetries.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Particles & Fields
Yui Hayashi et al.
Summary: This article studies the properties of self-duality symmetry in the Cardy-Rabinovici model. The self-duality is realized as a non-invertible symmetry due to complications in its realization, and at certain points, a mixed gravitational anomaly is detected. The article also explores how the phase diagram of the Cardy-Rabinovici model satisfies the anomaly matching condition.
JOURNAL OF HIGH ENERGY PHYSICS
(2022)
Article
Physics, Multidisciplinary
Lakshya Bhardwaj et al.
Summary: By gauging symmetries in quantum field theory, dual symmetries related to topological Wilson line defects can be obtained, forming a larger (d-1) × (d-1)-category. In one particular 2-category, the objects are 2d condensation defects constructed from higher-level gauging.
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
Inaki Garcia Etxebarria
Summary: N=4 supersymmetric Yang-Mills theories with algebra so(4N) and appropriate global structure choices can exhibit non-invertible symmetries. We identify the holographic dual branes associated with these non-invertible symmetries and derive the fusion rules for the symmetries from the branes' worldvolume dynamics.
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
Yichul Choi et al.
PHYSICAL REVIEW LETTERS
(2022)
Article
Astronomy & Astrophysics
Yichul Choi et al.
Summary: This study investigates non-invertible topological defects in quantum systems with higher-form global symmetry and explores their explicit realizations in various cases.
Article
Physics, Multidisciplinary
Ying-Hsuan Lin et al.
Summary: The fermionization of the Monster CFT with respect to Z2AZ2A is demonstrated.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Physics, Particles & Fields
Davide Gaiotto et al.
Summary: The article reviews the properties of orbifold operations in two-dimensional quantum field theories and discusses the Orbifold groupoids that control the composition of orbifold operations. Three-dimensional TQFT's of Dijkgraaf-Witten type are highlighted for their important role in the analysis. The extension to generalized symmetries and applications to constrain RG flows is briefly discussed.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Tzu-Chen Huang et al.
Summary: The paper discusses the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for three-point functions and lasso two-point functions are derived, and crossing symmetry is proven. The construction of regular TFTs for various fusion categories is provided, along with explanations on how non-regular TFTs can be obtained from regular TFTs through generalized gauging.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Mendel Nguyen et al.
Summary: The study examines a 3D lattice gauge theory with semi-Abelian gauge group, calculating mass gaps and string tensions using a monopole-gas description. It finds that the string tensions deviate from the N-ality rule and provide more information about the representations of the gauge group. The presence of non-invertible topological lines from the original Abelian theory explains this deviation, which is broken by adding W-bosons leading to the emergence of the N-ality rule in the deep infrared regime.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Zohar Komargodski et al.
Summary: The study revisits the symmetries of massless two-dimensional adjoint QCD with gauge group SU(N) and uncovers non-invertible symmetries severely constraining possible infrared phases and massive excitations. The theory enforces deconfinement of the fundamental quark through these new symmetries and exhibits soft breaking when the adjoint quark has a small mass. Additionally, the research delves into the dynamics of adjoint QCD deformed by symmetric quartic fermion interactions, suggesting partial confinement for the deformed theory and discussing emergent supersymmetry at nonzero mass.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Kansei Inamura
Summary: This study classifies 1+1d time-reversal invariant bosonic symmetry protected topological (SPT) phases with fusion category symmetry using topological field theories, showing that SPT phases are classified by equivalence classes of quintuples.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Particles & Fields
Ben Heidenreich et al.
Summary: It is believed that consistent theories of quantum gravity can be restored by broadening the concept of symmetry to include non-invertible topological operators, and the absence of these operators is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, the completeness of twist vortices defined by a discrete holonomy around their worldvolume has also been proven.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
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(2012)
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(2011)
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PHYSICAL REVIEW LETTERS
(2007)
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Juerg Froehlich et al.
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J Fröhlich et al.
PHYSICAL REVIEW LETTERS
(2004)
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D Friedan et al.
PHYSICAL REVIEW LETTERS
(2004)
Review
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E Fuchs et al.
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