Building MSSM Flux Vacua

TL;DR

This paper develops a concrete framework for Type IIB flux compactifications that are chiral, tadpole-free, and either N=1 or N=0, by combining magnetised D-branes on a Z2×Z2 orientifold with ISD G3 flux. The authors construct explicit global models whose low-energy sector includes MSSM-like physics, stabilized dilaton/complex structure moduli, and in some cases flux-induced soft SUSY breaking, while enforcing stringent K-theory tadpole constraints. They show how D-brane recombination can realize the MSSM from a left-right symmetric block and analyze the conditions under which exotics can be Higgsed away. The work also demonstrates the existence of N=1 flux vacua in backgrounds both with and without discrete torsion, discusses phenomenological features and soft terms, and outlines future directions toward de Sitter solutions, F-theory lifts, and broader landscape implications.

Abstract

We construct N=1 and N=0 chiral four-dimensional vacua of flux compactification in Type IIB string theory. These vacua have the common features that they are free of tadpole instabilities (both NSNS and RR) even for models with N=0 supersymmetry. In addition, the dilaton/complex structure moduli are stabilised and the supergravity background metric is warped. We present an example in which the low energy spectrum contains the MSSM spectrum with three generations of chiral matter. In the N=0 models, the background fluxes which stabilise the moduli also induce soft supersymmetry breaking terms in the gauge and chiral sectors of the theory, while satisfying the equation of motion. We also discuss some phenomenological features of these three generation MSSM flux vacua. Our techniques apply to other closed string backgrounds as well and, in fact, also allow to find new N=1 D-brane models which were believed not to exist. Finally, we discuss in detail the consistency conditions of these flux compactifications. Cancellation of K-theory charges puts additional constraints on the consistency of the models, which render some chiral D-brane models in the literature inconsistent.