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.
Highlights
The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of so-called twisted self-duality equations
A prominent example are Maxwell’s equations: Rather than expressing them in the standard form of second-order differential equations for a single gauge field, they may be written in terms of a gauge field and its magnetic dual by demanding that their respective field strengths are dual to each other
The price to pay for duality invariance is the abandonment of manifest general coordinate invariance of the action. The latter may be restored with a non-standard realization of space-time diffeomorphisms on the gauge fields
Summary
The dynamics of abelian vector and antisymmetric tensor gauge fields can be described in terms of so-called twisted self-duality equations. The price to pay for duality invariance is the abandonment of manifest general coordinate invariance of the action Not manifest, the latter may be restored with a non-standard realization of space-time diffeomorphisms on the gauge fields. The paper is organized as follows: in sections 2 and 3, we briefly review the general structure of the abelian twisted self-duality equations for vector gauge fields in four space-time dimensions, and the associated duality-invariant first-order action of [6, 7].
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