SUSY Breaking and Moduli Stabilization from Fluxes in Gauged 6D Supergravity

TL;DR

This paper constructs a 4D supergravity model from 6D supergravity with fluxes, demonstrating how moduli stabilization and supersymmetry breaking can occur in a setting resembling realistic string compactifications.

Contribution

It presents a simple 4D supergravity model derived from 6D supergravity with fluxes, incorporating moduli stabilization, supersymmetry breaking, and potential string theory origins.

Findings

Classical potential fixes the T modulus.

Perturbative corrections and gaugino condensation can lift the S flat direction.

The model predicts supersymmetry breaking with a positive cosmological constant.

Abstract

We construct the 4D N=1 supergravity which describes the low-energy limit of 6D supergravity compactified on a sphere with a monopole background a la Salam and Sezgin. This provides a simple setting sharing the main properties of realistic string compactifications such as flat 4D spacetime, chiral fermions and N=1 supersymmetry as well as Fayet-Iliopoulos terms induced by the Green-Schwarz mechanism. The matter content of the resulting theory is a supersymmetric SO(3)xU(1) gauge model with two chiral multiplets, S and T. The expectation value of T is fixed by the classical potential, and S describes a flat direction to all orders in perturbation theory. We consider possible perturbative corrections to the Kahler potential in inverse powers of $Re S$ and $Re T$, and find that under certain circumstances, and when taken together with low-energy gaugino condensation, these can lift the degeneracy of the flat direction for $Re S$. The resulting vacuum breaks supersymmetry at moderately low energies in comparison with the compactification scale, with positive cosmological constant. It is argued that the 6D model might itself be obtained from string compactifications, giving rise to realistic string compactifications on non Ricci flat manifolds. Possible phenomenological and cosmological applications are briefly discussed.