Flux Stabilization in 6 Dimensions: D-terms and Loop Corrections

TL;DR

This paper investigates flux-induced D-terms in 6D supergravity, exploring their role in moduli stabilization and potential uplift mechanisms, with implications for connecting string theory to 4D phenomenology.

Contribution

It provides a detailed analysis of flux-induced D-terms, one-loop corrections, and moduli stabilization mechanisms in 6D supergravity models, advancing understanding of string compactifications.

Findings

Flux-induced one-loop correction to scalar potential from charged hypermultiplets.

Explicit demonstration of D-term arising from gauging a compactification modulus.

Simultaneous stabilization of 6D dilaton and volume moduli using fluxes, gaugino condensation, and R-symmetry twist.

Abstract

We analyse D-terms induced by gauge theory fluxes in the context of 6-dimensional supergravity models. On the one hand, this is arguably the simplest concrete setting in which the controversial idea of `D-term uplifts' can be investigated. On the other hand, it is a very plausible intermediate step on the way from a 10d string theory model to 4d phenomenology. Our specific results include the flux-induced one-loop correction to the scalar potential coming from charged hypermultiplets. Furthermore, we comment on the interplay of gauge theory fluxes and gaugino condensation in the present context, demonstrate explicitly how the D-term arises from the gauging of one of the compactification moduli, and briefly discuss further ingredients that may be required for the construction of a phenomenologically viable model. In particular, we show how the 6d dilaton and volume moduli can be simultaneously stabilized, in the spirit of KKLT, by the combination of an R symmetry twist, a gaugino condensate, and a flux-induced D-term.