On D-brane moduli stabilisation

TL;DR

The paper argues that open-string moduli for space-time filling D-branes counted in a frozen background are not always unfixed once bulk dynamics are included. By analyzing D6-brane backreaction in compact spaces and deriving bilinear open–closed superpotentials, it shows that certain geometric and Wilson-line moduli are lifted by F-term potentials tied to flux quantisation. A microscopic mechanism based on backreaction and Page-charge quantisation explains how Wilson lines can backreact and acquire a stabilising potential, with a precise topological criterion involving two-cycles nontrivial in the ambient manifold. The approach extends to D7-branes in type IIB, yielding similar stabilization of Wilson lines and suggesting new avenues for string inflation and model-building via stabilized open-string sectors.

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.