Quarter-BPS solutions in three-dimensional N=16 supergravity and the Liouville equation

TL;DR

This paper derives Liouville equations from three-dimensional N=16 supergravity under supersymmetry assumptions, classifies solutions based on spinor properties, and shows solutions with fewer supersymmetries do not exist.

Contribution

It introduces a novel connection between supersymmetric solutions in supergravity and Liouville equations, providing a classification based on spinor analysis.

Findings

Liouville equations emerge from supersymmetry assumptions

Solutions with 6 or fewer supersymmetries do not exist

Classification of solutions via Spin(8) spinor analysis

Abstract

We show how by assuming at least 8 real timelike supersymmetries in the maximally supersymmetric three-dimensional ungauged supergravity and a further simplifying Ansatz, we are naturally led to a pair of Liouville field equations. We also show that there are no solutions that preserve only 6 real timelike supersymmetries. The solution relies on the classification of complex spinors of Spin(8) to which the problem quickly reduces.