Mink$_3\times S^3$ solutions of type II supergravity

TL;DR

This paper classifies supersymmetric solutions of type II supergravity on a specific 10D manifold, identifying known and new solutions, including a novel class with particular geometric features.

Contribution

It provides explicit local expressions for solutions with certain supersymmetry conditions, recovering known backgrounds and discovering new solutions within this framework.

Findings

Only known AdS4×S3 solution is the  background from D2-D6 branes.

Recovered various known brane configurations.

Discovered a new class of   imes S^2 imes S^3 solutions in IIA.

Abstract

We initiate the classification of supersymmetric solutions of type II supergravity on $\mathbb{R}^{1,2} \times S^3 \times M_4$. We find explicit local expressions for all backgrounds with either a single Killing spinor or two of equal norm, up to PDE's. We show that the only type II AdS$_4\times S^3$ solution is the known $\mathcal{N}=4$ AdS$_4$ background obtained from the near-horizon limit of intersecting D2-D6 branes. Various known branes and intersecting brane systems are recovered, and we obtain a novel class of $\mathbb{R}^{1,2} \times S^2\times S^3$ solutions in IIA.