AdS$_3\times$ S$^2$ in IIB with small ${\cal N}=(4,0)$ supersymmetry

TL;DR

This paper classifies warped AdS$_3\times$S$^2\times$M$_5$ backgrounds in type II supergravity with small ${\cal N}=(4,0)$ supersymmetry, deriving new classes of solutions in IIB supergravity with identity structure.

Contribution

It identifies and characterizes new classes of supersymmetric solutions in IIB supergravity with minimal isometries and identity structure, extending previous work on SU(2)-structure solutions.

Findings

In IIA, M$_5$ supports an SU(2)-structure, as previously studied.

In IIB, two broad new classes with identity structure are found.

The solutions are expressed through local PDEs and field expressions.

Abstract

We consider warped AdS$_3\times $S$^2\times$M$_5$ backgrounds in type II supergravity preserving small ${\cal N}=(4,0)$ supersymmetry. We show that imposing ${\cal N}=(4,0)$ supersymmetry imposes between 0 and 3 a priori isometries in the internal M$_5$. In this work we focus on classes of solution where M$_5$ exhibits no a prioi isometry which imposes additional constraints. Solving these in IIA forces M$_5$ to support an SU(2)-structure, a case already studied in arXiv:1908.09851, while in IIB one arrives at two broad new classes with identity structure that we reduce to local expressions for the physical fields and PDEs.