Higher-group structure in lattice Abelian gauge theory under instanton-sum modification

Abstract

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 $$\mathbb {Z}_q$$ Z q 1-form and $$\mathbb {Z}_p$$ Z p 3-form symmetries. Here, $$\mathbb {Z}_q$$ Z q is a subgroup of the center of U(1). Following the recent study of the lattice construction of the $$U(1)/\mathbb {Z}_q$$ U ( 1 ) / Z q principal bundle, we examine how such a structure is realized on the basis of lattice regularization.