Abstract
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 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.
Highlights
Since the question of discrete symmetries in theories of quantum gravity is a fundamental one, it is fair to address it in higher-dimensional theories
This paper explores a novel realization of discrete gauge symmetries in string theory,3 based on these higher rank gauge fields
String theory contains a plethora of higher rank antisymmetric tensor fields, which upon compactification pick up topological couplings generalizing (1.1)
Summary
We quickly review the realization of 4d discrete gauge symmetries as subgroups of ‘standard’ continuous gauge symmetries, i.e. carried by 1-form gauge fields. The description is phrased in terms of (a) a 1-form A1 and a 0-form φ, or (b) in a dual version, the magnetic gauge potential V1 and the 2-form B2 [5] (see [30] for an alternative viewpoint on discrete gauge symmetries). These are subject to gauge invariances (a) A1 → A1 + dλ , (b) B2 → B2 + dΛ1 , φ → φ+pλ V1 → V1 + p Λ1. We recall that for proper identification of the discrete symmetry, the normalization of B2 is such that its 4d dual scalar has periodicity 1, and that the minimal U(1) charge is 1
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