Noncompact gaugings, chiral reduction and dual sigma models in supergravity

TL;DR

This paper explores the structure of half-maximal SU(2) gauged supergravity with topological mass, its reduction to 6D, and the resulting matter couplings, revealing restrictions on higher-dimensional models and the geometry of scalar fields.

Contribution

It demonstrates the coupling of arbitrary vector multiplets in SU(2) gauged supergravity and analyzes the restrictions on 7D models for consistent 6D reductions, including matter scalar cosets.

Findings

Coupling of arbitrary vector multiplets in SU(2) gauged supergravity.

Restrictions on 7D models for 6D R-symmetry gauging.

Scalar fields parametrize specific coset spaces with abelian isometries.

Abstract

We show that the half-maximal SU(2) gauged supergravity with topological mass term admits coupling of an arbitrary number of n vector multiplets. The chiral circle reduction of the ungauged theory in the dual 2-form formulation gives N=(1,0) supergravity in 6D coupled to 3p scalars that parametrize the coset SO(p,3)/SO(p)x SO(3), a dilaton and (p+3) axions with p < n+1. Demanding that R-symmetry gauging survives in 6D is shown to put severe restrictions on the 7D model, in particular requiring noncompact gaugings. We find that the SO(2,2) and SO(3,1) gauged 7D supergravities give a U(1)_R, and the SO(2,1) gauged 7D supergravity gives an Sp(1)_R gauged chiral 6D supergravities coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p+1,4)/SO(p+1)x SO(4), with the (p+3) axions corresponding to its abelian isometries. In the ungauged 6D models, upon dualizing the axions to 4-form potentials, we obtain coupling of p linear multiplets and one special linear multiplet to chiral 6D supergravity.