Flux vacua in type IIB compactifications on orbifolds: their finiteness and minimal string coupling

TL;DR

This paper investigates the finiteness and properties of flux vacua in type IIB orbifold compactifications, showing bounds on string coupling and the impact of branes and fluxes on supersymmetry and vacuum count.

Contribution

It provides evidence for the finite number of flux vacua, characterizes the minimal string coupling in terms of flux, and explores how branes influence supersymmetry and bounds.

Findings

Finite number of inequivalent vacua for given flux charge

Minimal string coupling scales inversely with flux, g_s,min ~ c/N_flux^α

Negative D3-brane charge relaxes bounds and can break supersymmetry

Abstract

We perform a detailed study of (supersymmetric) moduli stabilisation in type IIB toroidal orientifolds with fluxes. We provide strong evidence towards exhaustion of the finite number of inequivalent vacua for a given total 3-form flux charge $N_{\rm flux}$. We also find that the minimal value of the string coupling $g_s$ is given in terms of $N_{\rm flux}$ and present strong evidence for the asymptotic relation $g_{s,\,\rm{min}}\sim c/N_{\rm flux}^\alpha$, with $\alpha=1,2$, valid for not too small $N_{\rm flux}$, where $c$ is an order 1 coefficient and $\alpha$ depends on the orbifold. Imposing tadpole cancellation, $N_{\rm flux}$ is bounded from the number of orientifold O3-planes. Combined with the flux quantisation, this forbids orientifold vacua without anti-brane charge. On the other hand, the presence of negative D3-brane charge induced by magnetised D7-branes breaks supersymmetry and relaxes the bound, allowing significantly smaller values for $g_s$.