Nonperturbative effects in the Standard Model with gauged 1-form symmetry

Anber, Mohamed M.; Poppitz, Erich

doi:10.1007/jhep12(2021)055

Cited by 18 publications

(8 citation statements)

References 33 publications

(112 reference statements)

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“…does not play a role in the ABJ anomaly. The matter content is consistent with the existence of an electric Z (1) 6 1-form global symmetry [54,55]. The cocycle conditions satisfied by SM on T 4 with a gauged Z (1) 6 are given by [55]:…”

Section: Jhep03(2024)169mentioning

confidence: 61%

Noninvertible symmetries and anomalies from gauging 1-form electric centers

Anber,

Chan

2024

J. High Energ. Phys.

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We devise a general method for obtaining 0-form noninvertible discrete chiral symmetries in 4-dimensional SU(N)/ℤp and SU(N) × U(1)/ℤp gauge theories with matter in arbitrary representations, where ℤp is a subgroup of the electric 1-form center symmetry. Our approach involves placing the theory on a three-torus and utilizing the Hamiltonian formalism to construct noninvertible operators by introducing twists compatible with the gauging of ℤp. These theories exhibit electric 1-form and magnetic 1-form global symmetries, and their generators play a crucial role in constructing the corresponding Hilbert space. The noninvertible operators are demonstrated to project onto specific Hilbert space sectors characterized by particular magnetic fluxes. Furthermore, when subjected to twists by the electric 1-form global symmetry, these surviving sectors reveal an anomaly between the noninvertible and the 1-form symmetries. We argue that an anomaly implies that certain sectors, characterized by the eigenvalues of the electric symmetry generators, exhibit multi-fold degeneracies. When we couple these theories to axions, infrared axionic noninvertible operators inherit the ultraviolet structure of the theory, including the projective nature of the operators and their anomalies. We discuss various examples of vector and chiral gauge theories that showcase the versatility of our approach.

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Section: Jhep03(2024)169mentioning

confidence: 61%

Noninvertible symmetries and anomalies from gauging 1-form electric centers

Anber,

Chan

2024

J. High Energ. Phys.

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“…We conclude this section by discussing the relationship between the configuration above and that of Kraan, van Baal, Lee, and Lu (KvBLL) [65][66][67][68][69][70][71][72][73][74][75]. Like ours, their solution carries magnetic charge and has nontrivial holonomy.…”

Section: E Simple Solutionmentioning

confidence: 82%

“…'t Hooft first presented explicit configurations on tori of finite volume [58][59][60][61][62][63][64]. Kraan, van Baal, Lee, and Lu [65][66][67][68][69][70][71][72][73][74][75] showed that at nonzero temperature instantons can be viewed as made of N constituents, each with topological charge 1/N ; the constituents have nontrival holonomy, and cannot be pulled arbitrarily far apart. Consequently, it is not apparent how these configurations survive in vacuum.…”

Section: Introductionmentioning

confidence: 99%

Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks

Nair¹,

Pisarski²

2022

Preprint

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In SU (N ) gauge theories without dynamical quarks, we discuss how configurations with fractional topological charge, ∼ 1/N , can arise in the vacuum and dominate in the confining phase. They are not solutions of the classical equations of motion, but arise as quantum solutions of the effective Lagrangian. Their size is essentially fixed, on the order of the confinement scale. We give both a general mathematical analysis and illustrative solutions. Their presence can be measured through numerical simulations on the lattice using known methods. As they carry ZN magnetic charge, the introduction of dynamical quarks significantly complicates their dynamics.

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“…A variety of authors have considered exotic gauged Z 3 symmetries to stabilize the proton in the context of the Minimal Supersymmetric Standard Model (MSSM) and extensions thereof (e.g., [14][15][16][17][18][19][20][21][22]), where baryon and lepton number are no longer classical global symmetries. Other interesting related work includes [23][24][25][26][27][28][29][30][31][32][33]. I note especially that, while conducting extensive literature review, I found that [34] on the global structure of the SM gauge group noted the existence of a Z N g anomaly-free subgroup of B/N c + L, and [35] on discrete symmetries in the MSSM mentioned in their Footnote 7 that a Z N g subgroup of B/N c protects the proton in the SM.…”

Section: Earlier Workmentioning

confidence: 99%

A Note on Proton Stability in the Standard Model

Koren

2022

Universe

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In this short note, we describe the symmetry responsible for absolute, nonperturbative proton stability in the Standard Model. The SM with Nc colors and Ng generations has an exact, anomaly-free, generation-independent, global symmetry group U(1)B−NcL×ZNgL, which contains a subgroup of baryon plus lepton number of order 2NcNg. This disallows proton decay for Ng>1. Many well-studied models beyond the SM explicitly break this global symmetry, and the alternative deserves further attention.

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Nonperturbative effects in the Standard Model with gauged 1-form symmetry

Abstract: We study the Standard Model with gauged $$ {\mathrm{\mathbb{Z}}}_{N=2,3,6}^{(1)} $$ ℤ N = 2 , 3 , 6 1 subgroups of its $$ {\mathrm{\mathbb{Z}}}_6^{(1)} $$ … Show more

Cited by 18 publications

References 33 publications

Noninvertible symmetries and anomalies from gauging 1-form electric centers

Noninvertible symmetries and anomalies from gauging 1-form electric centers

Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks

A Note on Proton Stability in the Standard Model

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