From ten to four and back again, generalizing the geometry

by Luca Martucci (LMU Munich)

Tuesday 11 Dec 2007, 14:00 → 15:30 Europe/Zurich

TH Theory Conference Room (CERN)

I will discuss the four-dimensional N=1 effective approach in the study of warped type II flux compactifications to AdS_4 or flat Minkowski space-time. Using a supergravity formulation invariant under local complexified Weyl transformations to accommodate the non-trivial warping, I will show how the resulting F-flatness and D-flatness equations exactly reproduce the full ten-dimensional supersymmetry equations. Furthermore, I will consider the effect of non-perturbative corrections to the superpotential arising from gaugino condensation or Euclidean D-brane instantons, showing how they induce a quantum deformation of the internal generalized geometry. Smeared instantons allow to understand KKLT-like AdS vacua from a ten-dimensional point of view. On the other hand, non-smeared instantons in IIB warped Calabi-Yau compactifications `destabilize' the Calabi-Yau complex structure into a genuine generalized complex one. This deformation gives a geometrical explanation of the non-trivial superpotential for mobile D3-branes induced by the non-perturbative corrections.