Higher-group structure in lattice Abelian gauge theory under instanton-sum modification

Kan, Naoto; Morikawa, Osamu; Nagoya, Yuta; Wada, Hiroo

doi:10.1140/epjc/s10052-023-11616-6

Cited by 9 publications

(3 citation statements)

References 24 publications

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“…1See also related recent studies [5][6][7][8][9][10][11][12][13][14][15][16] 2We find Refs. [17][18][19][20] on the microscopic approach in condensed matter physics.…”

Section: A Naive Dirac Equation With a Monopolementioning

confidence: 79%

A Microscopic study of Magnetic monopoles in Topological Insulators

Kan,

Aoki,

Fukaya

et al. 2024

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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In this article, we analyze a magnetic monopole in topological insulators. The monopole obtain a fractional electric charge because of the Witten effect. We consider this system with a microscopic view by adding the Wilson term to the ordinary Dirac Hamiltonian. The Wilson term yields the positive mass shift to the effective mass of the electrons, then the curved domain-wall is dynamically generated around the monopole. The zero-modes of the electrons are localized on the domain-wall, which can be identified as the source of the electric charge.

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“…1See also related recent studies [5][6][7][8][9][10][11][12][13][14][15][16] 2We find Refs. [17][18][19][20] on the microscopic approach in condensed matter physics.…”

Section: A Naive Dirac Equation With a Monopolementioning

confidence: 79%

A Microscopic study of Magnetic monopoles in Topological Insulators

Kan,

Aoki,

Fukaya

et al. 2024

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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“…( 10) takes a multiple of 𝑝. As we discuss from now, gauging not only the Z [1] 𝑁 symmetry (i.e., 𝐵 𝑝 ) but also the Z [3] 𝑝 symmetry at the same time, we can avoid this obstruction and observe the higher-group structure, that is, 4-group on the lattice [9,10].…”

Section: Instanton-sum Modification and Higher-group Structure In Lat...mentioning

confidence: 96%

“…For instance, on background Abelian gauge fields 𝐴 𝜇 and 𝐵 𝜇𝜈 , the gauge transformation acts as 𝐴 ↦ → 𝐴 + 𝑑𝜔, 𝐵 ↦ → 𝐵 + 𝑑𝜆 + 𝜔𝑑𝐴, and then such a mixture of symmetries is called the 2-group; as we know, this is similar to the Green-Schwarz mechanism.2 From our lattice viewpoint of generalized symmetries, as in Refs. [9,10], we can construct a 4-group structure in the lattice 𝑆𝑈 (𝑁) Yang-Mills theory with restricted topological sectors [11].…”

Section: Introductionmentioning

confidence: 99%

Higher-group symmetry in lattice gauge theories with restricted topological sectors

Morikawa,

Abe,

Kan

et al. 2023

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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In this paper, we give a brief overview of generalized symmetries from the point of view of the lattice regularization as a fully regularized framework. At first, we illustrate the generalization of 't Hooft anomaly matching for higher-form symmetries. Furthermore the main interest goes to the higher-group symmetry. In particular, we find that the so-called 4-group appears in the lattice Yang-Mills theory under modification of instanton sum.

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Effective brane field theory with higher-form symmetry

Hidaka,

Kawana

2024

J. High Energ. Phys.

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We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

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Higher-group structure in lattice Abelian gauge theory under instanton-sum modification

Cited by 9 publications

References 24 publications

A Microscopic study of Magnetic monopoles in Topological Insulators

A Microscopic study of Magnetic monopoles in Topological Insulators

Higher-group symmetry in lattice gauge theories with restricted topological sectors

Effective brane field theory with higher-form symmetry

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