F-theory Flux Vacua and Attractor Equations

TL;DR

This paper explores the distribution of flux vacua in F-theory and Type IIB compactifications, demonstrating their connection to attractor equations and analyzing the behavior of non-supersymmetric solutions.

Contribution

It provides the first explicit demonstration that flux vacua in F-theory satisfy generalized attractor equations, linking moduli stabilization to supergravity attractor mechanisms.

Findings

Distribution of non-supersymmetric flux vacua decreases with string coupling

Flux vacua solutions satisfy generalized attractor equations

The flux vacua distribution suggests a deep connection with supergravity attractors

Abstract

We examine the vacuum structure of 4D effective theories of moduli fields in spacetime compactifications with quantized background fluxes. Imposing the no-scale structure for the volume deformations, we numerically investigate the distributions of flux vacua of the effective potential in complex structure moduli and axio-dilaton directions for two explicit examples in Type IIB string theory and F-theory compactifications. It turns out that distributions of non-supersymmetric flux vacua exhibit a non-increasing functional behavior of several on-shell quantities with respect to the string coupling. We point out that this phenomena can be deeply connected with a previously-reported possible correspondence between the flux vacua in moduli stabilization problem and the attractor mechanism in supergravity, and our explicit demonstration implies that such a correspondence generically exist even in the framework of F-theory. In particular, we confirm that the solutions of the effective potential we explicitly evaluated in Type IIB and F-theory flux compactifications indeed satisfy the generalized form of the attractor equations simultaneously.