Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries

Katsura, Hosho; Nakayama, Yu

doi:10.1007/jhep08(2022)072

Cited by 9 publications

(3 citation statements)

References 47 publications

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“…codimension invertibility topologicalness ordinary symmetry = 1 ✓ ✓ higher-form/group sym [1, ≥ 1 ✓ ✓ non-invertible/categorical sym = 1 ✗ ✓ higher categorical sym ≥ 1 ✗ ✓ subsystem sym [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91] = 1 ✓ ✗ higher subsystem sym [141][142][143][144][145][146][147][148][149][150][151][152] ≥ 1 ✓ ✗ subsystem non-invertible sym = 1 ✗ ✗ higher subsystem non-invertible sym ≥ 1 ✗ ✗…”

Section: Symmetrymentioning

confidence: 99%

“…The remaining symmetries differ in one or multiple properties. For instance, higher-form symmetries relax the condition of codimension being one [1,; 1 non-invertible symmetries in (1 + 1)d relax the invertibility ; subsystem symmetries in (2 + 1)d relax the topologicalness or the mobility of the symmetry generators/defects 2 [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91]. 3 Here and in Tab.…”

Section: Introduction 1subsystem Non-invertible Symmetrymentioning

confidence: 99%

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Subsystem non-invertible symmetry operators and defects

Cao,

Li,

Yamazaki

et al. 2023

SciPost Phys.

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We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z_2ℤ2 symmetry. We introduce a subsystem \mathbb Z_2ℤ2-gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers-Wannier transformation. The corresponding duality operators and defects are constructed by gaugings on the whole or half of the Hilbert space. By gauging twice, we derive fusion rules of duality operators and defects, which enriches ordinary Ising fusion rules with subsystem features. Subsystem Kramers-Wannier duality defects are mobile in both spatial directions, unlike the defects of invertible subsystem symmetries. We finally comment on the anomaly of the subsystem Kramers-Wannier duality symmetry, and discuss its subtleties.

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Section: Symmetrymentioning

confidence: 99%

Section: Introduction 1subsystem Non-invertible Symmetrymentioning

confidence: 99%

Subsystem non-invertible symmetry operators and defects

Cao,

Li,

Yamazaki

et al. 2023

SciPost Phys.

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“…While fracton phases first appeared in lattice systems, one would also expect a continuum description in the low-energy limit of a lattice system. There have been proposed such descriptions by continuum quantum field theories (QFTs) in various situations [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The QFTs do not have the Lorentz invariance or even the full rotational invariance, and can have the discontinuous field configurations.…”

Section: Introductionmentioning

confidence: 99%

Foliated-exotic duality in fractonic BF theories

Ohmori

Shimamura

2023

SciPost Phys.

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There has been proposed two continuum descriptions of fracton systems: foliated quantum field theories (FQFTs) and exotic quantum field theories. Certain fracton systems are believed to admit descriptions by both, and hence a duality is expected between such a class of FQFTs and exotic QFTs. In this paper we study this duality in detail for concrete examples in 2+12+1 and 3+13+1 dimensions. In the examples, both sides of the continuum theories are of BFBF-type, and we find the explicit correspondences of gauge-invariant operators, gauge fields, parameters, and allowed singularities and discontinuities. This deepens the understanding of dualities in fractonic quantum field theories.

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Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions

Honda

Nakanishi

2023

J. High Energ. Phys.

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We study various non-relativistic field theories with exotic symmetries called subsystem symmetries, which have recently attracted much attention in the context of fractons. We start with a scalar theory called ϕ-theory in d + 1 dimensions and discuss its properties studied in literature for d ≤ 3 such as self-duality, vacuum structure, ’t Hooft anomaly, anomaly inflow and lattice regularization. Next we study a theory called chiral ϕ-theory which is an analogue of a chiral boson with subsystem symmetries. Then we discuss theories including fermions with subsystem symmetries. We first construct a supersymmetric version of the ϕ-theory and dropping its bosonic part leads us to a purely fermionic theory with subsystem symmetries called ψ-theory. We argue that lattice regularization of the ψ-theory generically suffers from an analogue of doubling problem as previously pointed out in the d = 3 case. We propose an analogue of Wilson fermion to avoid the “doubling” problem. We also supersymmetrize the chiral ϕ-theory and dropping the bosonic part again gives us a purely fermionic theory. We finally discuss vacuum structures of the theories with fermions and find that they are infinitely degenerate because of spontaneous breaking of subsystem symmetries.

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Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries

Cited by 9 publications

References 47 publications

Subsystem non-invertible symmetry operators and defects

Subsystem non-invertible symmetry operators and defects

Foliated-exotic duality in fractonic BF theories

Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions

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