N = 1, D = 6 Supergravity: Duality and non Minimal Couplings

TL;DR

This paper develops a superspace formulation for N=1, D=6 supergravity with dualities and non-minimal couplings, including the Green-Schwarz mechanism, expanding understanding of supergravity theories with tensor multiplets.

Contribution

It introduces a superspace formulation for N=1, D=6 supergravity with dual forms and analyzes conditions for non-minimal couplings, including the Green-Schwarz anomaly cancellation.

Findings

Dual formulations of supergravity fields are compatible with supersymmetry.

Non-minimal couplings can be consistent with duality transformations.

The Green-Schwarz mechanism is incorporated into the supergravity framework.

Abstract

In this paper we present a superspace formulation of $N = 1, D = 6$ supergravity with one tensor-multiplet and an arbitrary number of vector- and hypermultiplets, in which the bosonic abelian superforms of the theory, the dilaton, the abelian gauge fields and the two-form are replaced by their S-duals i.e. four, three and two-superforms respectively, in compatibility with supersymmetry. As usual this replacement interchanges Bianchi identities with equations of motion. This formulation holds in the presence of one tensor multiplet and arbitrary numbers of hypermultiplets and abelian super-Maxwell multiplets if all couplings are minimal. We determine the consistency conditions for non-minimal couplings in $N = 1$, $D = 6$ supergravity, for which we present a particularly significant solution, namely the one associated with the Chern-Simons-Lorentz three-form which entails the Green-Schwarz anomaly cancellation mechanism. In the case of non minimal couplings it is found that the gauge fields and the two-form can still be dualized while the dilaton has to remain a zero-form.