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

TL;DR

This paper explores higher-group symmetries in lattice gauge theories, demonstrating the emergence of 4-group structures in modified instanton sum scenarios within lattice Yang--Mills theory.

Contribution

It introduces the concept of higher-group symmetry in lattice gauge theories and shows how a 4-group arises in modified instanton sum conditions.

Findings

Higher-form symmetry anomaly matching generalized

Identification of 4-group symmetry in lattice Yang--Mills

Framework for analyzing topological sectors in lattice theories

Abstract

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.