Duality Symmetric Actions with Manifest Space-Time Symmetries

TL;DR

This work addresses the challenge of formulating duality symmetries, including electric–magnetic (and related string dualities), at the level of a space-time covariant action. It introduces an auxiliary vector field $u_m(x)$ from an axion sector and a two-form $\Lambda_{mn}$ to build a covariant, duality-symmetric action for a Maxwell field, drawing on PST-like ideas; it also generalizes the construction to the heterotic string’s low-energy bosonic sector with manifest $SL(2,R)\times O(6,22)$ symmetry. The authors present a duality-symmetric Maxwell action with a self-dual tensor ${\cal F}^\alpha_{mn}$ and show equivalence to standard Maxwell theory upon appropriate gauge fixing of $u_m$; they further extend to 28 abelian gauge fields with matrices ${\cal M}$ and $M$, achieving manifest duality and space-time symmetry and reducing to the Schwarz–Sen form in a particular gauge. This covariant framework provides a unified route to duality invariance in gauge theories and string compactifications, with potential supersymmetric extensions and generalizations to other dimensions.

Abstract

We consider a space-time invariant duality symmetric action for a free Maxwell field and an $SL(2,{\bf R})\times SO(6,22)$ invariant effective action describing a low-energy bosonic sector of the heterotic string compactified on a six-dimensional torus. The manifest Lorentz and general coordinate invariant formulation of the models is achieved by coupling dual gauge fields to an auxiliary vector field from an axionic sector of the theory.