An introduction to decomposition

Sharpe, Eric

doi:10.48550/arxiv.2204.09117

Cited by 9 publications

(13 citation statements)

References 45 publications

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“…Decomposition [1] is now understood as the statement that a d-dimensional quantum field theory with a global (d − 1)-form symmetry is equivalent to a disjoint union of other ddimensional quantum field theories, known as universes (see e.g. [2] for a recent review). Typical examples include two-dimensional gauge theories with trivially-acting subgroups of the gauge group [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Decomposition, Condensation Defects, and Fusion

Robbins

Sharpe

2022

Fortschritte der Physik

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In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher-form symmetry along a submanifold, and so there is a natural interplay with notions of decomposition, the statement that d-dimensional quantum field theories with global (d − 1)-form symmetries are equivalent to disjoint unions of other quantum field theories. We will also construct new (sometimes non-invertible) defects, and compute their fusion products, again utilizing decomposition. An important role will be played in all these analyses by theta angles for gauged higher-form symmetries, which can be used to select individual universes in a decomposition.

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Section: Introductionmentioning

confidence: 99%

“…Decomposition has been applied in a number of contexts, see e.g. [2] for a recent overview. In this paper, we will apply decomposition to condensation defects, defined in [10,11] as follows.…”

Section: Introductionmentioning

confidence: 99%

Decomposition, Condensation Defects, and Fusion

Robbins

Sharpe

2022

Fortschritte der Physik

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“…Other applications of the symmetry-extension construction on the (1 + 1)D gauge theories and orbifolds can be found in a recent survey [184].…”

Section: Symmetry Extensionmentioning

confidence: 99%

Symmetric Mass Generation

Wang

You

2022

Symmetry

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The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG.

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“…Other applications of the symmetry-extension construction on the (1+1)D gauge theories and orbifolds can be found in a recent survey [173].…”

Section: No Table VIII Summary Of the Symmetry-extension Construction...mentioning

confidence: 99%

Symmetric Mass Generation

Wang,

You

2022

Preprint

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The most well-known mechanism for fermions to acquire a mass is the Nambu-Goldstone-Anderson-Higgs mechanism, i.e. after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group. This new mechanism is generally referred to as the "Symmetric Mass Generation (SMG)." It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes current numerical results, introduces a novel unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and overviews various features and applications of SMG.

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An introduction to decomposition

Cited by 9 publications

References 45 publications

Decomposition, Condensation Defects, and Fusion

Decomposition, Condensation Defects, and Fusion

Symmetric Mass Generation

Symmetric Mass Generation

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