Topology of SU(N) lattice gauge theories coupled with ℤ N 2-form gauge fields

Abstract We extend the definition of Lüscher’s lattice topological charge to the case of 4d SU(N) gauge fields coupled with ℤ N 2-form gauge fields. This result is achieved while maintaining the locality, the SU(N) gauge invariance, and 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 ℤ N 1-form symmetry and the θ periodicity.