Abstract
We consider the U(1) gauge theory on a four-dimensional torus, where the instanton number is restricted to an integral multiple of p. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green–Schwarz mechanism, between mathbb {Z}_q 1-form and mathbb {Z}_p 3-form symmetries. Here, mathbb {Z}_q is a subgroup of the center of U(1). Following the recent study of the lattice construction of the U(1)/mathbb {Z}_q principal bundle, we examine how such a structure is realized on the basis of lattice regularization.
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