General Type IIB Fluxes with SU(3) Structures

TL;DR

This paper derives solutions for supersymmetric vacua in type IIB supergravity with SU(3) structures, revealing conditions on fluxes, internal manifold geometry, and the role of holomorphic functions in these solutions.

Contribution

It provides the first explicit solutions to supersymmetric flux vacua with SU(3) structures, linking geometric constraints to flux configurations and holomorphic functions.

Findings

Internal manifold must be complex

Holomorphic function determines solution form

Type-A and type-B vacua identified near poles and zeros

Abstract

A supersymmetric vacuum has to obey a set of constraints on fluxes as well as first order differential equations defined by the G-structures of the internal manifold. We solve these equations for type IIB supergravity with SU(3) structures. The 6-dimensional internal manifold has to be complex, the axion/dilaton is in general non-holomorphic and a cosmological constant is only possible if the SU(3) structures are broken to SU(2) structures. The general solution is expressed in terms of one function which is holomorphic in the three complex coordinates and if this holomorphic function is constant, we obtain a flow-type solution and near poles and zeros we find the so-called type-A and type-B vacuum.