Gauged locally supersymmetric D=3 nonlinear sigma models

TL;DR

The paper develops a comprehensive framework for gauged locally supersymmetric D=3 nonlinear sigma models by augmenting pure 3D supergravity with a Chern-Simons term and gauging a subgroup of sigma-model isometries, possibly including R-symmetry. It introduces an embedding-tensor formalism that yields a $T$-tensor encoding the gauging data, and derives the precise supersymmetry constraints that ensure consistency, including the central condition that $T^{IJ,KL}$ avoids a specific ${ m SO}(N)$ irrep. The authors provide explicit constructions of the ${A_1,A_2,A_3}$ tensors and the scalar potential $V$ across $N=1$ to $N=4$, and extend the analysis to higher $N$ by exploiting the symmetric-space structure of target manifolds to classify admissible gauge groups via a projection on the embedding tensor. The work delivers a complete classification of gauged 3D supergravities, with concrete examples of gauge groups for $N>4$ (including exceptional and noncompact groups) and a clear route to AdS$_3$ vacua and their holographic implications.

Abstract

We construct supersymmetric deformations of general, locally supersymmetric, nonlinear sigma models in three spacetime dimensions, by extending the pure supergravity theory with a Chern-Simons term and gauging a subgroup of the sigma model isometries, possibly augmented with R-symmetry transformations. This class of models is shown to include theories with standard Yang-Mills Lagrangians, with optional moment interactions and topological mass terms. The results constitute a general classification of three-dimensional gauged supergravities.