Covariant actions for N=1, D=6 Supergravity theories with chiral bosons

TL;DR

This paper develops covariant, supersymmetric actions for six-dimensional theories with chiral bosons using the PST framework. By introducing an auxiliary scalar a and the related fields v^a, the authors construct S_0^{±} and combine them with S_6 to yield covariant actions for a single tensor multiplet, pure N=1 D=6 supergravity, and N=1 D=6 supergravity coupled to n tensor multiplets, while ensuring closure of the SUSY algebra and consistency with the required bosonic symmetries. The approach is compatible with superspace techniques, extends to interacting tensor multiplets via the coset SO(1,n)/SO(n), and highlights constraints on Yang–Mills couplings to preserve locality and supersymmetry, with potential extensions to IIB supergravity in D=10. Overall, it provides a structured, covariant Lagrangian framework for chiral bosons in 6D SUSY/SUGRA and clarifies the role of the auxiliary field a and the K^{(±)} tensors in maintaining both covariance and supersymmetry.

Abstract

We show that the recently found covariant formulation for chiral $p$--forms in $2(p+1)$ dimensions with $p$ even, can be naturally extended to supersymmetric theories. We present the general method for writing covariant actions for chiral bosons and construct, in particular, in six dimensions covariant actions for one tensor supermultiplet, for pure supergravity and for supergravity coupled to an arbitrary number of tensor supermultiplets.