Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Koide, Masataka; Nagoya, Yuta; Yamaguchi, Satoshi

doi:10.48550/arxiv.2109.05992

Cited by 12 publications

(22 citation statements)

References 37 publications

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“…The phase transitions at θ = ±π mod 4π are transitions between these two low-energy phases. Our result is in agreement with [20], where a non-invertible defect was found in a lattice model which exhibits the same phase transition. 4 For w T X 5 1 to be non-vanishing X 5 must be unorientable, but we will assume X 4 to be orientable and spin.…”

Section: Examplessupporting

confidence: 92%

“…For the particular cases we study, the resulting non-invertible defect will be shown to be a generalization of the Kramers-Wannier defect in (1+1)d. Our defects will have similar implications for self-duality of the gauge theories. Our result can be seen as a continuum analog of the Kramers-Wannier duality of lattice Z 2 gauge theories in (3+1)-dimensions [5], whose corresponding defect has been studied in [20].…”

mentioning

confidence: 64%

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Kramers-Wannier-like duality defects in (3+1)d gauge theories

Kaidi,

Ohmori,

Zheng

2021

Preprint

182

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We introduce a class of non-invertible 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. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU (2) super YM at τ = i. We also introduce an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories.

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Section: Examplessupporting

confidence: 92%

mentioning

confidence: 64%

Kramers-Wannier-like duality defects in (3+1)d gauge theories

Kaidi,

Ohmori,

Zheng

2021

Preprint

182

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“…These are operators that, like more familiar symmetries, do not change under small deformations of their positions, but whose fusion algebra is more general than that of a group. These non-invertible symmetries have recently been explored in [53,54,[66][67][68][69][70][71]. Other arguments for conditions similar to (3.29) have appeared in [50][51][52].…”

Section: Non-abelian Weak Gravity and Non-invertible Symmetrymentioning

confidence: 99%

Generalized Symmetry Breaking Scales and Weak Gravity Conjectures

Córdova¹,

Ohmori²,

Rudelius³

2022

Preprint

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We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the magnetic and axion versions of the weak gravity conjecture can be motivated by the assumption that generalized global symmetries should be strongly broken within the context of low-energy effective field theory, i.e. at a characteristic scale less than the Planck scale where quantum gravity effects become important. For example, the assumption that the electric one-form symmetry of Maxwell theory should be strongly broken below the Planck scale implies the weak gravity conjecture. Similarly, the violation of generalized non-invertible symmetries is closely tied to analogs of this conjecture for non-abelian gauge theory. This reasoning enables us to unify these conjectures with the absence of global symmetries in quantum gravity.

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“…for all h ∈ H. 7 In the subsequent sections, we will use the string diagram notation where the above conditions 1-5 are represented as follows:…”

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confidence: 99%

On lattice models of gapped phases with fusion category symmetries

Inamura

2021

Preprint

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We construct topological quantum field theories (TQFTs) and commuting projector Hamiltonians for any 1+1d gapped phases with non-anomalous fusion category symmetries, i.e. finite symmetries that admit SPT phases. The construction is based on two-dimensional state sum TQFT whose input datum is an H-simple left H-comodule algebra, where H is a finite dimensional semisimple Hopf algebra. We show that the actions of fusion category symmetries C on the boundary conditions of these state sum TQFTs are represented by module categories over C. This agrees with the classification of gapped phases with symmetry C. We also find that the commuting projector Hamiltonians for these state sum TQFTs have fusion category symmetries at the level of the lattice models and hence provide lattice realizations of gapped phases with fusion category symmetries. As an application, we discuss the edge modes of SPT phases based on these commuting projector Hamiltonians. Finally, we mention that we can extend the construction of topological field theories to the case of anomalous fusion category symmetries by replacing a semisimple Hopf algebra with a semisimple pseudo-unitary connected weak Hopf algebra.

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Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Cited by 12 publications

References 37 publications

Kramers-Wannier-like duality defects in (3+1)d gauge theories

Kramers-Wannier-like duality defects in (3+1)d gauge theories

Generalized Symmetry Breaking Scales and Weak Gravity Conjectures

On lattice models of gapped phases with fusion category symmetries

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