On AdS$_3$ solutions of Type IIB

TL;DR

This paper analyzes supersymmetric AdS$_3$ solutions in Type IIB supergravity with non-trivial fluxes and $SU(3)$-structure, deriving conditions for supersymmetry and a generalized master equation for solutions.

Contribution

It provides necessary and sufficient supersymmetry conditions and introduces a generalized master equation for solving the equations of motion in this context.

Findings

Derived supersymmetry constraints on torsion classes.

Formulated a generalized master equation for flux solutions.

Clarified conditions for consistent AdS$_3$ backgrounds.

Abstract

We study $\mathcal{N}=1$ supersymmetric AdS$_3 \times M_7$ backgrounds of Type IIB supergravity, with non-vanishing axio-dilaton, three-form and five-form fluxes, and a "strict" $SU(3)$-structure on $M_7$. We derive the necessary and sufficient conditions for supersymmetry as a set of constraints on the torsion classes of the $SU(3)$-structure. Given an Ansatz for the three-form fluxes, the problem of also solving the equations of motion involves a "master equation", which generalizes ones that have previously appeared in the literature.