Flux Vacua Attractors and Generalized Compactifications

TL;DR

This paper analytically confirms the existence of supersymmetric attractor equations for certain flux vacua in string compactifications and explores their generalizations to non-Kähler geometries.

Contribution

It verifies analytically that flux attractor equations lead to supersymmetric minima and clarifies their potential generalizations to non-Kähler compactifications.

Findings

Confirmed supersymmetric minima for type IIB flux vacua.

Derived attractor equations for N=1 Minkowski vacua in specific string theories.

Clarified the scope of attractor equations beyond Kähler manifolds.

Abstract

We investigate whether there are attractor equations for N=1 flux vacua in generalized compactifications. We fill a gap in the existing literature by verifying analytically that the recently proposed susy attractors, for type IIB CY(3) orientifold compactifications with flux, do give supersymmetric minima of the relevant scalar potential. Furthermore, our considerations clarify various confusions about existing proposals for generalization of the flux vacua attractors to non-K\"{a}hler compactifications. We explore different possibilities for generalization and find attractor equations for N=1 Minkowski vacua only both for the heterotic string on SU(3) structure manifolds and for type IIA/B on SU(3)xSU(3) structure spaces.