General Type IIB Fluxes with SU(3) Structures

TL;DR

This work provides a complete, SUSY-consistent analysis of general Type IIB flux vacua with $SU(3)$ structures. The internal six-manifold must be complex, the axio-dilaton is generally non-holomorphic, and a 4D cosmological constant is forbidden unless SU(3) is enhanced to SU(2); the entire solution is encoded by a single holomorphic function $f(z^i)$, with the external geometry remaining Minkowski when SUSY is preserved. When $f$ is constant, the solutions describe RG-flow–like backgrounds, while poles and zeros of $f$ correspond to type-A and type-B vacua, respectively; the authors also discuss special Hermitian/Kähler limits and how the master function is fixed by the equations of motion and Bianchi identities. The framework bridges fluxes, intrinsic torsion classes, and warp factors to deliver explicit expressions for the axio-dilaton $ au$, warp factors, and fluxes, enabling connections to AdS/CFT and potential brane realizations through the holomorphic data $f$. Overall, the paper delivers a systematic, explicit parametrization of ${ m IIB}$ flux vacua with ${ m SU}(3)$ structure, clarifying how geometry, fluxes, and holomorphic data shape four-dimensional physics and its moduli stabilization prospects.

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.