Warped generalized geometry compactifications, effective theories and non-perturbative effects

TL;DR

This paper explores four-dimensional effective theories for type II flux compactifications with SU(3)x SU(3) structures, emphasizing warp factors, supersymmetry conditions, and non-perturbative effects like instantons and gaugino condensation.

Contribution

It introduces a supergravity formulation invariant under local complexified Weyl transformations and connects ten-dimensional supersymmetry equations with four-dimensional superpotential and Kaehler potential, including non-perturbative corrections.

Findings

Warp factor leads to supergravity invariance under complexified Weyl transformations.

Supersymmetry equations derived from superpotential and Kaehler potential.

Non-perturbative effects explain KKLT-like vacua and D3-brane superpotentials.

Abstract

Summarizing the results of arXiv:0707.1038, we discuss the four-dimensional effective approach to type II N=1 supersymmetric flux compactifications with general SU(3)x SU(3)-structure. In particular, we study the effect of a non-trivial warp factor, which we argue leads naturally to a supergravity formulation invariant under local complexified Weyl transformations. We show that the full ten-dimensional supersymmetry equations can be obtained as F-flatness and D-flatness conditions from the superpotential and Kaehler potential. We then consider non-perturbative corrections to these supersymmetry conditions, following from adding instanton or gaugino condensation effects to the superpotential. As examples, we show how smeared instantons allow to understand the ten-dimensional geometry of KKLT-like AdS vacua and we give an explanation for the superpotential for "mobile" D3-branes in terms of a non-perturbatively induced generalized complex structure.