Topology of $SU(N)$ lattice gauge theories coupled with ${\mathbb{Z}}_N$ $2$-form gauge fields

Abstract

We extend the definition of Lüscher's lattice topological charge to the case of $4$d $SU(N)$ gauge fields coupled with ${\mathbb{Z}}_N$ $2$-form gauge fields. This result is achieved while maintaining the locality, the $SU(N)$ gauge invariance, and ${\mathbb{Z}}_N$ $1$-form gauge invariance, and we find that the manifest $1$-form gauge invariance plays the central role in our construction. This result gives the lattice regularized derivation of the mixed 't Hooft anomaly in pure $SU(N)$ Yang-Mills theory between its ${\mathbb{Z}}_N$ $1$-form symmetry and the $\theta$ periodicity.

20 pages, 3 figures; (v2) minor improvements, refs updated

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Cited by in corpus (4)

• Remarks on Geometric Engineering, Symmetry TFTs and Anomalies
• Instanton Density Operator in Lattice QCD from Higher Category Theory
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• 't Hooft line in 4D $U(1)$ lattice gauge theory and a microscopic description of dyon's statistics