The Superconformal Gaugings in Three Dimensions

TL;DR

This paper demonstrates how to derive three-dimensional superconformal theories with up to eight supersymmetries from gauged supergravity models, introducing new theories based on exceptional Lie superalgebras and analyzing their constraints.

Contribution

It provides a systematic method to obtain superconformal theories from gauged supergravity and introduces new theories based on exceptional Lie superalgebras.

Findings

Derived superconformal theories for N ≤ 8 from gauged supergravity.

Identified new N=4,5 superconformal theories based on exceptional Lie superalgebras.

Analyzed constraints and solutions for embedding tensors in these theories.

Abstract

We show how three-dimensional superconformal theories for any number N <= 8 of supersymmetries can be obtained by taking a conformal limit of the corresponding three-dimensional gauged supergravity models. The superconformal theories are characterized by an embedding tensor that satisfies a linear and quadratic constraint. We analyze these constraints and give the general solutions for all cases. We find new N = 4,5 superconformal theories based on the exceptional Lie superalgebras F(4), G(3) and D(2|1;\alpha). Using the supergravity connection we discuss which massive deformations to expect. As an example we work out the details for the case of N = 6 supersymmetry.