Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications

TL;DR

This paper explores nonperturbative superpotentials in flux compactifications, focusing on gaugino condensation effects in F-theory on K3×K3, and discusses their role in moduli stabilization.

Contribution

It provides an explicit example of gaugino condensation generating superpotentials in flux compactifications, expanding understanding beyond Euclidean brane instantons.

Findings

Flux stabilizes D7 branes and lifts matter fields.

Gaugino condensation occurs on cycles with genus ≥ 1.

Flux allows divisors with higher genus to contribute to superpotentials.

Abstract

There are two known sources of nonperturbative superpotentials for K\"ahler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The first class of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on $K3 \times K3$ with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation, and generate a nonperturbative superpotential for K\"ahler moduli. We describe how the relevant geometries in general contain cycles of arithmetic genus $\chi \geq 1$ (and how $\chi > 1$ divisors can contribute to the superpotential, in the presence of flux). This second class of effects is likely to be important in finding even larger classes of models where the KKLT mechanism of moduli stabilization can be realized. We also address various claims about the situation for IIB models with a single K\"ahler modulus.