(3+1)D path integral state sums on curved U(1) bundles and U(1) anomalies of (2+1)D topological phases

Kobayashi, Ryohei; Barkeshli, Maissam

doi:10.48550/arxiv.2111.14827

Cited by 6 publications

(12 citation statements)

References 50 publications

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“…Moreover, a recent work Ref. [31] provides a general analysis on the coupling between (2+1)d topological orders and general curved U(1) background gauge fields. Establishing the relation between the analysis in Ref.…”

Section: Discussionmentioning

confidence: 99%

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Gauging U(1) symmetry in (2+1)d topological phases

Cheng,

Jian

2022

Preprint

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We study the gauging of a global U(1) symmetry in a gapped system in (2+1)d. The gauging procedure has been well-understood for a finite global symmetry group, which leads to a new gapped phase with emergent gauge structure and can be described algebraically using the mathematical framework of modular tensor category (MTC). We develop a categorical description of U(1) gauging in a MTC, taking into account the dynamics of U(1) gauge field absent in the finite group case. When the ungauged system has a non-zero Hall conductance, the gauged theory remains gapped and we determine the complete set of anyon data for the gauged theory. On the other hand, when the Hall conductance vanishes, we argue that gauging has the same effect of condensing a special Abelian anyon nucleated by inserting 2π U(1) flux. We apply our procedure to the SU(2) k MTCs and derive the full MTC data for the Z k parafermion MTCs. We also discuss a dual U(1) symmetry that emerges after the original U(1) symmetry of an MTC is gauged.

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Section: Discussionmentioning

confidence: 99%

“…Establishing the relation between the analysis in Ref. [31] and our general framework for U(1) symmetry gauging (where the U(1) gauge field becomes dynamical) will be left for future work.…”

Section: Discussionmentioning

confidence: 99%

Gauging U(1) symmetry in (2+1)d topological phases

Cheng,

Jian

2022

Preprint

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“…See for example Refs. [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. In particular, based on the idea of G-crossed braided fusion categories [27], Refs.…”

Section: Relation To Prior Workmentioning

confidence: 99%

Anomaly of $(2+1)$-dimensional symmetry-enriched topological order from $(3+1)$-dimensional topological quantum field theory

Zou

2023

SciPost Phys.

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Symmetry acting on a (2+1)DD topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)DD on-site symmetry. In this paper, we develop a (3+1)DD topological quantum field theory to calculate the anomaly indicators of a (2+1)DD topological order with a general symmetry group GG, which may be discrete or continuous, Abelian or non-Abelian, contain anti-unitary elements or not, and permute anyons or not. These anomaly indicators are partition functions of the (3+1)DD topological quantum field theory on a specific manifold equipped with some GG-bundle, and they are expressed using the data characterizing the topological order and the symmetry actions. Our framework is applied to derive the anomaly indicators for various symmetry groups, including \mathbb{Z}_2\times\mathbb{Z}_2ℤ2×ℤ2, \mathbb{Z}_2^T\times\mathbb{Z}_2^Tℤ2T×ℤ2T, SO(N)SO(N), O(N)^TO(N)T, SO(N)\times \mathbb{Z}_2^TSO(N)×ℤ2T, etc, where \mathbb{Z}_2ℤ2 and \mathbb{Z}_2^Tℤ2T denote a unitary and anti-unitary order-2 group, respectively, and O(N)^TO(N)T denotes a symmetry group O(N)O(N) such that elements in O(N)O(N) with determinant -1−1 are anti-unitary. In particular, we demonstrate that some anomaly of O(N)^TO(N)T and SO(N)\times \mathbb{Z}_2^TSO(N)×ℤ2T exhibit symmetry-enforced gaplessness, i.e., they cannot be realized by any symmetry-enriched topological order. As a byproduct, for SO(N)SO(N) symmetric topological orders, we derive their SO(N)SO(N) Hall conductance.

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“…Moreover, a recent work Ref. [32] provides a general analysis on the coupling between (2+1)d topological orders and general curved U(1) background gauge fields. Establishing the relation between the analysis in Ref.…”

Section: Dual U(1) Dual Symmetry After U(1) Gaugingmentioning

confidence: 99%

“…Establishing the relation between the analysis in Ref. [32] and our general framework for U(1) symmetry gauging (where the U(1) gauge field becomes dynamical) will be left for future work.…”

Section: Dual U(1) Dual Symmetry After U(1) Gaugingmentioning

confidence: 99%

Gauging U(1) symmetry in (2+1)d topological phases

Cheng

Jian

2022

SciPost Phys.

View full text Add to dashboard Cite

We study the gauging of a global U(1) symmetry in a gapped system in (2+1)d. The gauging procedure has been well-understood for a finite global symmetry group, which leads to a new gapped phase with emergent gauge structure and can be described algebraically using the mathematical framework of modular tensor category (MTC). We develop a categorical description of U(1) gauging in a MTC, taking into account the dynamics of U(1) gauge field absent in the finite group case. When the ungauged system has a non-zero Hall conductance, the gauged theory remains gapped and we determine the complete set of anyon data for the gauged theory. On the other hand, when the Hall conductance vanishes, we argue that gauging has the same effect of condensing a special Abelian anyon nucleated by inserting 2\pi2π U(1) flux. We apply our procedure to the SU(2)_kk MTCs and derive the full MTC data for the \mathbb{Z}_kℤk parafermion MTCs. We also discuss a dual U(1) symmetry that emerges after the original U(1) symmetry of an MTC is gauged.

show abstract

(3+1)D path integral state sums on curved U(1) bundles and U(1) anomalies of (2+1)D topological phases

Cited by 6 publications

References 50 publications

Gauging U(1) symmetry in (2+1)d topological phases

Gauging U(1) symmetry in (2+1)d topological phases

Anomaly of $(2+1)$-dimensional symmetry-enriched topological order from $(3+1)$-dimensional topological quantum field theory

Gauging U(1) symmetry in (2+1)d topological phases

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