Stability of flux vacua in the presence of charged black holes

TL;DR

The paper analyzes whether a charged black hole can perturb moduli stabilization in Type IIB flux compactifications near a deformed conifold. By linking the matrix-model prepotential to the conifold limit, it shows that the black-hole contribution to the moduli minimum is typically negligible, being suppressed as $\sim 1/(Q^{2} q^{2})$, and that flux-induced stabilization near the conifold is robust but can admit small, exceptional shifts if charges/fluxes are tiny or finely tuned. It also demonstrates a close structural similarity between black-hole attractor equations and flux-stabilization equations, enabling a unified, matrix-model–inspired view of the combined system. The work points to minor but potentially important corrections in limited parameter regimes and outlines directions for a full ten-dimensional, warped-analysis and quantum corrections via matrix-model methods.

Abstract

In this letter we consider a charged black hole in a flux compactification of type IIB string theory. Both the black hole and the fluxes will induce potentials for the complex structure moduli. We choose the compact dimensions to be described locally by a deformed conifold, creating a large hierarchy. We demonstrate that the presence of a black hole typically will not change the minimum of the moduli potential in a substantial way. However, we also point out a couple of possible loop-holes, which in some cases could lead to interesting physical consequences such as changes in the hierarchy.