A Goldstone theorem for continuous non-invertible symmetries

Etxebarria, Iñaki García; Iqbal, Nabil

doi:10.1007/jhep09(2023)145

Cited by 34 publications

(5 citation statements)

References 51 publications

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“…N and magnetic U N 1-form global center symmetry, and the immediate exercise would be checking whether there is a mixed anomaly between the center and the noninvertible chiral symmetries. To this end, we turn on both electric and magnetic twists 17 (m, k) ∈ Z 6 , giving rise to nonabelian fractional topological charge Q SU(N ) ∈ Z/N as well as abelian topological charge Q u = n N 2 ; see eq. (2.15).…”

Section: Jhep03(2024)169mentioning

confidence: 99%

Noninvertible symmetries and anomalies from gauging 1-form electric centers

Anber,

Chan

2024

J. High Energ. Phys.

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We devise a general method for obtaining 0-form noninvertible discrete chiral symmetries in 4-dimensional SU(N)/ℤp and SU(N) × U(1)/ℤp gauge theories with matter in arbitrary representations, where ℤp is a subgroup of the electric 1-form center symmetry. Our approach involves placing the theory on a three-torus and utilizing the Hamiltonian formalism to construct noninvertible operators by introducing twists compatible with the gauging of ℤp. These theories exhibit electric 1-form and magnetic 1-form global symmetries, and their generators play a crucial role in constructing the corresponding Hilbert space. The noninvertible operators are demonstrated to project onto specific Hilbert space sectors characterized by particular magnetic fluxes. Furthermore, when subjected to twists by the electric 1-form global symmetry, these surviving sectors reveal an anomaly between the noninvertible and the 1-form symmetries. We argue that an anomaly implies that certain sectors, characterized by the eigenvalues of the electric symmetry generators, exhibit multi-fold degeneracies. When we couple these theories to axions, infrared axionic noninvertible operators inherit the ultraviolet structure of the theory, including the projective nature of the operators and their anomalies. We discuss various examples of vector and chiral gauge theories that showcase the versatility of our approach.

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Section: Jhep03(2024)169mentioning

confidence: 99%

Noninvertible symmetries and anomalies from gauging 1-form electric centers

Anber,

Chan

2024

J. High Energ. Phys.

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“…These form a A N,−T L minimal theory, which we consider screened on the boundary. 24 The coupled twist defect is described by:…”

Section: 24)mentioning

confidence: 99%

“Zoology” of non-invertible duality defects: the view from class $$ \mathcal{S} $$

Antinucci,

Copetti,

Galati

et al. 2024

J. High Energ. Phys.

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We study generalizations of the non-invertible duality defects present in $$ \mathcal{N} $$ N = 4 SU(N) SYM by studying theories with larger duality groups. We focus on 4d $$ \mathcal{N} $$ N = 2 theories of class $$ \mathcal{S} $$ S obtained by the dimensional reduction of the 6d $$ \mathcal{N} $$ N = (2, 0) theory of AN−1 type on a Riemann surface Σg without punctures. We discuss their non-invertible duality symmetries and provide two ways to compute their fusion algebra: either using discrete topological manipulations or a 5d TQFT description. We also introduce the concept of “rank” of a non-invertible duality symmetry and show how it can be used to (almost) completely fix the fusion algebra with little computational effort.

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“…These works go beyond previous constructions in their analysis of the resulting symmetry structure in terms of so-called higher representations of higher groups [7,56,71]. Finally, these types of non-invertible symmetries have been further discussed in the context of various typical quantum field theories such as free field theories [99], pure gauge theories [2,88], quantum electrodynamics [75], axion models [34] and within other physical contexts [30,32,33,35,69].…”

Section: Introductionmentioning

confidence: 99%

Higher categorical symmetries and gauging in two-dimensional spin systems

Delcamp,

Tiwari

2024

SciPost Phys.

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We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries. Our framework relies on an approach to dualities whereby dual quantum lattice models only differ in a choice of module 2-category over some input fusion 2-category. Given an arbitrary two-dimensional spin system with an ordinary symmetry, we explain how to perform the (twisted) gauging of any of its sub-symmetries. We then demonstrate that the resulting model has a symmetry structure encoded into the Morita dual of the input fusion 2-category with respect to the corresponding module 2-category. We exemplify this approach by specialising to certain finite group generalisations of the transverse-field Ising model, for which we explicitly define lattice symmetry operators organised into fusion 2-categories of higher representations of higher groups.

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A Goldstone theorem for continuous non-invertible symmetries

Cited by 34 publications

References 51 publications

Noninvertible symmetries and anomalies from gauging 1-form electric centers

Noninvertible symmetries and anomalies from gauging 1-form electric centers

“Zoology” of non-invertible duality defects: the view from class $$ \mathcal{S} $$

Higher categorical symmetries and gauging in two-dimensional spin systems

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