A massive class of $\mathcal{N} = 2$ AdS$_4$ IIA solutions

TL;DR

This paper classifies a broad class of $ abla=2$ supersymmetric AdS$_4$ solutions in massive type IIA supergravity, deriving new solutions with complex internal spaces and analyzing their geometric and physical properties.

Contribution

It provides a systematic classification of $ abla=2$ AdS$_4$ solutions with SU(2) structure, including new analytical solutions with various singularities and physical features.

Findings

Derived a Riccati ODE for complex internal spaces and solved it analytically.

Discovered numerous new regular solutions and solutions with localized O8-planes.

Reproduced many known solutions within the new classification framework.

Abstract

We initiate a classification of $\mathcal{N} =2$ supersymmetric AdS$_4$ solutions of (massive) type IIA supergravity. The internal space is locally equipped with either an SU(2) or an identity structure. We focus on the SU(2) structure and determine the conditions it satisfies, dictated by supersymmetry. Imposing as an Ansatz that the internal space is complex, we reduce the problem of finding solutions to a Riccati ODE, which we solve analytically. We obtain in this fashion a large number of new families of solutions, both regular as well as with localized O8-planes and conical Calabi--Yau singularities. We also recover many solutions already discussed in the literature.