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

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 $N_{\mathrm{flux}}$. We also find that the minimal value of the string coupling $g_s$ is given in terms of $N_{\mathrm{flux}}$ and present strong evidence for the asymptotic relation $g_{s,\min }\sim c/N_{\mathrm{flux}}^{\alpha }$, with $\alpha =1,2$, valid for not too small $N_{\mathrm{flux}}$, where $c$ is an order 1 coefficient and $\alpha$ depends on the orbifold. Imposing tadpole cancellation, $N_{\mathrm{flux}}$ 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 $g_s$.

arXiv comment54 pages, 3 figures. v2: minor corrections, added references. v3: published version, minor corrections + correction factor 1/2 in tadpole conditions

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• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme