Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

Article Physics, Multidisciplinary

Non-invertible topological defects in 4-dimensional Z2 pure lattice gauge theory

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)

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Article Physics, Mathematical

Anomaly Inflow and p-Form Gauge Theories

Chang-Tse Hsieh et al.

Summary: The focus of this study is on the gravitational and Green-Schwarz type anomalies of chiral and non-chiral p-form gauge fields. These anomalies naturally arise as boundary modes of higher-dimensional bulk topological phases. By computing the Atiyah-Patodi-Singer eta-invariant, we provide a systematic description of the total bulk-boundary system, analogous to the realization of a chiral fermion on the boundary of a massive fermion. The SL(2, Z) anomaly of the 4D Maxwell theory is determined using our formalism, and we also investigate the worldvolume theories of D-branes and M5-branes in different string, M, and F theories.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2022)

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Article Physics, Multidisciplinary

Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories

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)

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Article Physics, Particles & Fields

Self-dual U(1) lattice field theory with a θ-term

Mariia Anosova et al.

Summary: In this paper, we study U(1) gauge theories with a modified Villain action and discuss their coupling to electric and magnetic matter as well as the exact electric-magnetic duality. We also show that imposing electric-magnetic duality results in a local, but not ultra-local lattice action.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

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Article Physics, Particles & Fields

On lattice models of gapped phases with fusion category symmetries

Kansei Inamura

Summary: We construct a topological quantum field theory (TQFT) model to describe 1+1d gapped phases with non-anomalous fusion category symmetries. By using module categories, we show how fusion category symmetries act on the boundary conditions of the TQFT. We also find that the commuting projector Hamiltonians of the TQFT have fusion category symmetries at the lattice model level, thus providing lattice realizations of gapped phases with fusion category symmetries.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

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Article Physics, Particles & Fields

Phase structure of self-dual lattice gauge theories in 4d

Mariia Anosova et al.

Summary: This paper discusses U(1) lattice gauge theory models based on a modified Villain formulation, which allows coupling to bosonic electric and magnetic matter. The formulation demonstrates duality mapping electric and magnetic sectors. Several generalizations of the models are proposed and their 't Hooft anomalies are discussed. Particularly interesting theories are those where electric and magnetic matter fields are coupled with identical actions, and the theory exhibits a self-dual symmetry. Numerical simulations are conducted on the simplest case with exactly one electrically and one magnetically charged boson to analyze the phase structure and nature of the self-dual symmetry.

JOURNAL OF HIGH ENERGY PHYSICS (2022)

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Article Astronomy & Astrophysics

Noninvertible duality defects in 3+1 dimensions

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.

PHYSICAL REVIEW D (2022)

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Article Physics, Particles & Fields

Orbifold groupoids

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)

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Article Physics, Particles & Fields

Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

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)

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Article Physics, Particles & Fields

Symmetries and strings of adjoint QCD2

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)

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Article Physics, Particles & Fields

Topological field theories and symmetry protected topological phases with fusion category symmetries

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)

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Article Astronomy & Astrophysics

Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory

Mendel Nguyen et al.

Summary: In 2D Yang-Mills theory, exact Casimir scaling leads to infinitely many string tensions due to nonpropagating gluons. The richness in the spectrum of string tensions, seemingly mysterious from ordinary symmetry considerations, cannot be explained by finite center symmetry. By introducing a noninvertible 1-form symmetry, a discrepancy between dynamics and kinematics is resolved, with potential implications for Yang-Mills theories in 3D and 4D.

PHYSICAL REVIEW D (2021)

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Article Astronomy & Astrophysics

Ising model as a U(1) lattice gauge theory with a θ-term

Tin Sulejmanpasic

Summary: In this study, a gauged XY model with a theta term on an arbitrary lattice in 1 + 1 dimensions is discussed. It is found that in the limit of strong gauge coupling, the theory exactly reduces to the 2d Ising model on the dual lattice, provided that the topological term is defined through the Villain action. The duality is generalized to higher-dimensional Ising models using higher-form U(1) gauge field analogs, and the phase diagram is analyzed by comparing strong and weak gauge coupling limits. Simulation results at intermediate couplings are also presented.

PHYSICAL REVIEW D (2021)

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Article Physics, Particles & Fields

Topological aspects of 4D Abelian lattice gauge theories with the θ parameter

Masazumi Honda et al.

JOURNAL OF HIGH ENERGY PHYSICS (2020)

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Article Physics, Particles & Fields

Topological operators and completeness of spectrum in discrete gauge theories

Tom Rudelius et al.

JOURNAL OF HIGH ENERGY PHYSICS (2020)

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Article Physics, Multidisciplinary

Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions

Wenjie Ji et al.

PHYSICAL REVIEW RESEARCH (2020)

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Article Physics, Multidisciplinary

First-Principles Simulations of 1+1D Quantum Field Theories at θ = π and Spin Chains

Tin Sulejmanpasic et al.

PHYSICAL REVIEW LETTERS (2020)

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Article Physics, Multidisciplinary

Anomalies in the space of coupling constants and their dynamical applications I

Clay Cordova et al.

SCIPOST PHYSICS (2020)

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Article Physics, Multidisciplinary

Anomalies in the space of coupling constants and their dynamical applications II

Clay Cordova et al.

SCIPOST PHYSICS (2020)

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Article Physics, Particles & Fields

Abelian gauge theories on the lattice: θ-Terms and compact gauge theory with(out) monopoles

Tin Sulejmanpasic et al.

NUCLEAR PHYSICS B (2019)

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Article Physics, Particles & Fields

The bi-fundamental gauge theory in 3+1 dimensions: the vacuum structure and a cascade

Avner Karasik et al.

JOURNAL OF HIGH ENERGY PHYSICS (2019)

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Article Physics, Particles & Fields

Dai-Freed anomalies in particle physics

Inaki Garcia-Etxebarria et al.

JOURNAL OF HIGH ENERGY PHYSICS (2019)

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Article Physics, Multidisciplinary

Anomaly of the Electromagnetic Duality of Maxwell Theory

Chang-Tse Hsieh et al.

PHYSICAL REVIEW LETTERS (2019)

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Article Physics, Particles & Fields

Topological defect lines and renormalization group flows in two dimensions

Chi-Ming Chang et al.

JOURNAL OF HIGH ENERGY PHYSICS (2019)

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Article Physics, Particles & Fields

On finite symmetries and their gauging in two dimensions

Lakshya Bhardwaj et al.

JOURNAL OF HIGH ENERGY PHYSICS (2018)

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Article Physics, Particles & Fields

Time-reversal breaking in QCD4, walls, and dualities in 2+1 dimensions

Davide Gaiotto et al.

JOURNAL OF HIGH ENERGY PHYSICS (2018)

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Article Physics, Multidisciplinary

Anomalies of duality groups and extended conformal manifolds

Nathan Seiberg et al.

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS (2018)

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Article Physics, Particles & Fields

Dual simulation of the 2d U(1) gauge Higgs model at topological angle θ = π : Critical endpoint behavior

Christof Gattringer et al.

NUCLEAR PHYSICS B (2018)

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Article Materials Science, Multidisciplinary

Anomaly and global inconsistency matching: θ angles, SU(3)/U(1)2 nonlinear sigma model, SU(3) chains, and generalizations

Yuya Tanizaki et al.

PHYSICAL REVIEW B (2018)

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Article Physics, Particles & Fields

Vacuum structure of bifundamental gauge theoriesat finitet opological angles

Yuya Tanizaki et al.

JOURNAL OF HIGH ENERGY PHYSICS (2017)

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Article Physics, Particles & Fields

Theta, time reversal and temperature

Davide Gaiotto et al.

JOURNAL OF HIGH ENERGY PHYSICS (2017)

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Article Physics, Multidisciplinary

Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics

Yuta Kikuchi et al.

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS (2017)

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Article Physics, Mathematical

Anyonic Chains, Topological Defects, and Conformal Field Theory

Matthew Buican et al.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2017)

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Article Physics, Multidisciplinary

Topological defects on the lattice: I. The Ising model

David Aasen et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2016)

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Article Physics, Particles & Fields

Generalized global symmetries

Davide Gaiotto et al.

JOURNAL OF HIGH ENERGY PHYSICS (2015)

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Article Physics, Particles & Fields

Topological field theory on a lattice, discrete theta-angles and confinement

Anton Kapustin et al.

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS (2014)

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Article Physics, Particles & Fields

Coupling a QFT to a TQFT and duality

Anton Kapustin et al.

JOURNAL OF HIGH ENERGY PHYSICS (2014)

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Article Physics, Particles & Fields

Reading between the lines of four-dimensional gauge theories

Ofer Aharony et al.

JOURNAL OF HIGH ENERGY PHYSICS (2013)

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Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

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