Fluxes, supersymmetry breaking and gauged supergravity

TL;DR

The paper interprets flux compactifications of type II string theories as gauged supergravity in four dimensions, showing how p-form fluxes gauge axionic shift symmetries to produce a scalar potential that stabilizes moduli and can yield partial supersymmetry breaking. It develops the duality-gauging framework, highlighting how $Sp(2n_V,\mathbb{R})$ transformations constrain admissible gaugings and how axion gaugings lead to nilpotent, solvable algebras acting on vector fields. It then applies this to concrete $T_6$ and $K3\times T_2$ orientifolds, detailing the corresponding nilpotent algebras $N_p$, the resulting scalar potentials, and the patterns of supersymmetry breaking and moduli stabilization, including no-scale-like vacua and specific flux-induced vacua with partial breaking. The results illustrate controlled mechanisms for moduli stabilization and SUSY breaking within extended supergravity, shaped by the algebraic structure of the gauged translational isometries.

Abstract

We report on the gauged supergravity interpretation of certain compactifications of superstring theories with p-form fluxes turned on. We discuss in particular the interplay of duality symmetries in type IIB orientifolds and gauged isometries in the corresponding supergravity models. Turning on fluxes is generally described by the gauging of some nilpotent Lie group whose generators correspond to axion symmetries of R-R and N-S scalars.

Figures (1)

• Figure 1: $SO(6,6)$ Dynkin diagrams for the $T_{p-3}\times T_{9-p}$ models. The shaded sub-diagrams define the groups $SL(p-3, \mathbb{R})\times SL(9-p,\mathbb{R})$ acting transitively on the metric moduli. The empty circles define simple roots corresponding to the metric moduli $g_{ij},\,g_{ab}$, the gray circle denotes a simple root corresponding to a Kalb--Ramond field $B_{ia}$ and the black circle corresponds to a R--R axion.