On D-brane moduli stabilisation

TL;DR

This paper challenges the conventional counting of D-brane moduli in string compactifications, showing that some moduli are lifted by bulk effects, which has implications for string model building and inflation.

Contribution

It demonstrates that bulk backreaction and flux effects lift certain open string moduli, revising the standard moduli counting in D-brane compactifications.

Findings

Some geometric and Wilson line moduli are lifted before instanton effects.

D-brane backreaction and flux quantisation cause moduli lifting.

New mechanisms for inflation model building in string theory are proposed.

Abstract

Standard results in 4d N=1 string compactifications assign a number of moduli to each space-time filling D-brane, computed by analysing the D-brane action in a fixed background. We revisit such conventional wisdom and argue that this naive counting of open string moduli is incorrect, in the sense that some of them will be lifted when making dynamical the bulk degrees of freedom. We explicitly discuss this effect for D6-branes wrapping special Lagrangian three-cycles, showing that some geometric and Wilson line moduli are lifted even before taking into account worldsheet instanton effects. From a 4d effective theory viewpoint the moduli lifting is due to an F-term potential, and can be deduced from the superpotentials in the literature. From a microscopic viewpoint the lifting is due to D-brane backreaction effects and flux quantisation in a compact manifold, and provides a mechanism for lifting Wilson line moduli. The latter applies to certain D6-branes and D7-brane Wilson lines, yielding new possibilities to build models of inflation in string theory.