Actions for Non-Abelian Twisted Self-Duality

TL;DR

This paper develops a non-abelian extension of twisted self-duality actions for gauge fields, introducing couplings to higher-rank tensors, with potential applications in Yang-Mills and supergravity theories.

Contribution

It presents the first non-abelian generalization of twisted self-duality actions, incorporating couplings to higher-rank tensor fields and analyzing their implications.

Findings

Non-abelian twisted self-duality equations derived.

Couplings to higher-rank tensor fields introduced.

Potential applications to Yang-Mills and supergravity discussed.

Abstract

The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of twisted self-duality equations. These first-order equations relate the p-form fields to their dual forms by demanding that their respective field strengths are dual to each other. It is well known that such equations can be integrated to a local action that carries on equal footing the p-forms together with their duals and is manifestly duality invariant. Space-time covariance is no longer manifest but still present with a non-standard realization of space-time diffeomorphisms on the gauge fields. In this paper, we give a non-abelian generalization of this first-order action by gauging part of its global symmetries. The resulting field equations are non-abelian versions of the twisted self-duality equations. A key element in the construction is the introduction of proper couplings to higher-rank tensor fields. We discuss possible applications (to Yang-Mills and supergravity theories) and comment on the relation to previous no-go theorems.