Antisymmetric tensor Z_p gauge symmetries in field theory and string theory

TL;DR

The paper investigates discrete gauge symmetries in D dimensions that arise from breaking continuous gauge symmetries carried by higher-rank antisymmetric tensors, not just 1-forms. It develops a field-theory framework with an $r$-form $A_r$ and an $(r-1)$-form $\phi_{r-1}$, including dual descriptions, which yields a residual ${\bf Z}_p$ after a Higgs-like mechanism. It provides concrete Lagrangians, dualities, and string-theory realizations via flux catalysis and torsion, showing that charged defects are branes of various dimensionalities and that non-abelian discrete groups can emerge from brane intersections. These results broaden the understanding of discrete gauge symmetries in quantum gravity and offer new links between brane charge classifications (K-theory) and topological discrete sectors, with potential holographic applications.

Abstract

We consider discrete gauge symmetries in D dimensions arising as remnants of broken continuous gauge symmetries carried by general antisymmetric tensor fields, rather than by standard 1-forms. The lagrangian for such a general ${\bf Z}_p$ gauge theory can be described in terms of a $r$-form gauge field made massive by a $(r-1)$-form, or other dual realizations, that we also discuss. The theory contains charged topological defects of different dimensionalities, generalizing the familiar charged particles and strings in D=4. We describe realizations in string theory compactifications with torsion cycles, or with background field strength fluxes. We also provide examples of non-abelian discrete groups, for which the group elements are associated with charged objects of different dimensionality.