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

TL;DR

This work formulates a warped, four-dimensional N=1 effective theory for type II flux compactifications with general SU(3)×SU(3) structure using generalized complex geometry. It shows that warped backgrounds admit a local complexified Weyl-invariant (superconformal) description, with the SUSY conditions arising from F-flatness and D-flatness of a 4D supergravity defined by a holomorphic superpotential and a conformal Kähler potential. Non-perturbative effects from instantons or gaugino condensation modify the SUSY equations and enable KKLT-like AdS vacua via smeared instantons, while also providing a ten-dimensional interpretation of nonperturbatively induced generalized complex structures that generate D3-brane superpotentials. Altogether, the paper connects 10D SUSY conditions to a warped 4D effective framework and clarifies how non-perturbative physics shapes moduli stabilization and D3-brane dynamics in these geometries.

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.