Type IIB Supersymmetric Flux Vacua

TL;DR

This paper investigates supersymmetric flux vacua in Type IIB string theory on toroidal orientifolds, revealing constraints on flux contributions and tadpole cancellation, and constructing semi-realistic models with relaxed tadpole conditions.

Contribution

It demonstrates the impossibility of simultaneously having positive moduli and negative flux contributions in Minkowski vacua, and constructs semi-realistic AdS models with relaxed tadpole conditions.

Findings

Positive flux contributions are necessary for stabilized Minkowski vacua.

Relaxed tadpole conditions are achievable in AdS vacua but not in Minkowski vacua.

Constructed a semi-realistic Pati-Salam model from flux compactifications.

Abstract

On the Type IIB toroidal T^6 orientifolds with generic flux compactifications, we conjecture that in generic supsersymmetric Minkowski vacua, at least one of the flux contributions to the seven-brane and D3-brane tadpoles is positive if the moduli are stabilized properly, and then the tadpole cancellation conditions can not be relaxed. To study the supsersymmetric Minkowski flux vacua, we simplify the fluxes reasonably and discuss the corresponding superpotential. We show that we can not have simultaneously the positive real parts of all the moduli and the negative/zero flux contributions to all the seven-brane and D3-brane tadpoles. Therefore, we can not construct realistic flux models with the relaxed tadpole cancellation conditions. When studying the supsersymmetric AdS vacua, we obtain flux models with the seven-brane and D3-brane tadpole cancellation conditions relaxed elegantly, and we present a semi-realistic Pati-Salam model as well as its particle spectrum. The lifting from the AdS vacua to the Minkowski/dS vacua remains a great challenge in flux model buildings on toroidal orientifolds.