All supersymmetric solutions of minimal supergravity in six dimensions

TL;DR

This work achieves a complete local classification of all supersymmetric solutions in minimal six-dimensional supergravity by exploiting Killing spinor bilinears and $G$-structure methods. The authors derive a general local metric form with a null Killing vector $V$, an almost hyper-Kähler base ${\cal B}$, and a controlled expansion of the self-dual 3-form $G$, all governed by equations on ${\cal B}$. They identify several important special cases, including non-twisting, $u$-independent, and Gibbons–Hawking base solutions, and show how six harmonic functions can specify broad families of solutions with a rich structure. A key result is the near-horizon geometry classification for supersymmetric horizons, which restricts possibilities to $\mathbb{R}^{1,1}\times T^4$, $\mathbb{R}^{1,1}\times K3$, or identified $AdS_3\times S^3$, and they establish that the only maximally supersymmetric backgrounds are $\mathbb{R}^{1,5}$, $AdS_3\times S^3$, and a maximally supersymmetric plane wave. The findings illuminate the links to five-dimensional theories via dimensional reduction and lay groundwork for exploring gauged six-dimensional theories and higher-dimensional generalizations.

Abstract

A general form for all supersymmetric solutions of minimal supergravity in six dimensions is obtained. Examples of new supersymmetric solutions are presented. It is proven that the only maximally supersymmetric solutions are flat space, AdS_3 x S^3 and a plane wave. As an application of the general solution, it is shown that any supersymmetric solution with a compact horizon must have near-horizon geometry R^{1,1} x T^4, R^{1,1} x K3 or identified AdS_3 x S^3.