Complex structure moduli stability in toroidal compactifications

TL;DR

This paper classifies the dynamics and stability of complex structure moduli in toroidal compactifications of Type II string theories, focusing on how D-branes and tadpole terms influence moduli stabilization and decay scenarios.

Contribution

It provides a detailed analysis of moduli stabilization in specific toroidal compactifications, highlighting the effects of D-branes and potential terms on stability and decay pathways.

Findings

Stable solutions exist within the moduli space for certain configurations.

Moduli can be driven to the boundary of the moduli space, indicating instability.

Some configurations lead to decay into a set of branes.

Abstract

In this paper we present a classification of possible dynamics of closed string moduli within specific toroidal compactifications of Type II string theories due to the NS-NS tadpole terms in the reduced action. They appear as potential terms for the moduli when supersymmetry is broken due to the presence of D-branes. We particularise to specific constructions with two, four and six-dimensional tori, and study the stabilisation of the complex structure moduli at the disk level. We find that, depending on the cycle on the compact space where the brane is wrapped, there are three possible cases: i) there is a solution inside the complex structure moduli space, and the configuration is stable at the critical point, ii) the moduli fields are driven towards the boundary of the moduli space, iii) there is no stable solution at the minimum of the potential and the system decays into a set of branes.