On The Supersymmetric Solutions of D=3 Half-maximal Supergravities

TL;DR

This paper systematically studies supersymmetric solutions in three-dimensional half-maximal supergravity, revealing their geometric structure, dualities, and explicit solutions for different Killing vector cases.

Contribution

It introduces a detailed analysis of Killing spinor invariant tensors in 3D supergravity, connecting scalar geometry and dualities, and provides explicit solutions for timelike and null Killing vectors.

Findings

Scalar current reduces to covariant holomorphicity equations.

Explicit solutions for timelike Killing vectors.

General pp-wave solutions for null Killing vectors.

Abstract

We initiate a systematic study of the solutions of three-dimensional matter-coupled half-maximal (N=8) supergravities which admit a Killing spinor. To this end we analyze in detail the invariant tensors built from spinor bilinears, a technique originally developed and applied in higher dimensions. This reveals an intriguing interplay with the scalar target space geometry SO(8,n)/(SO(8) x SO(n)). Another interesting feature of the three-dimensional case is the implementation of the duality between vector and scalar fields in this framework. For the ungauged theory with timelike Killing vector, we explicitly determine the scalar current and show that its integrability relation reduces to a covariant holomorphicity equation, for which we present a number of explicit solutions. For the case of a null Killing vector, we give the most general solution which is of pp-wave type.