From ten to four and back again: how to generalize the geometry

By Paul Koerber, L. Martucci. 2007

208 citations recorded by the source corpus.

We discuss the four-dimensional N = 1 effective approach in the study of warped type II flux compactifications with SU(3) × SU(3)-structure to AdS4 or flat Minkowski space-time. The non-trivial warping makes it natural to use a supergravity formulation invariant under local complexified Weyl transformations. We obtain the classical superpotential from a standard argument involving domain walls and generalized calibrations and show how the resulting F-flatness and D-flatness equations exactly reproduce the full ten-dimensional supersymmetry equations. Furthermore, we consider the effect of non-perturbative corrections to this superpotential arising from gaugino condensation or Euclidean D-brane instantons. For the latter we derive the supersymmetry conditions in N = 1 flux vacua in full generality. We find that the non-perturbative corrections 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.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f66da081da9545fbcbab058b27a87cf926b6c356

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Citations in the corpus

D3-brane potentials from fluxes in AdS/CFT (2010, background): “Another ten-dimensional description of nonperturbative effects was given in [27], where a generalized complex geometry was argued to encode the nonperturbative superpotential in the decompactification limit.”
Smeared versus localised sources in flux compactifications (2010, background): “One way to incorporate the changes that arise upon localising a source is through “warped effective field theory” [7–18], in which one derives the correction to the fourdimensional effective action.”
MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND F-THEORY: A REVIEW (2012, background): “This is compatible with the observation that the flux can not lead to supersymmetric Minkowski solutions because it is known that the non-perturbative effects deform the 10-dimensional solution away from CY and lead to supersymmetric AdS solutions [39,289].”
The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets (2008, methodology): “Here we will follow the approach of [32], which calculated the superpotential and the (conformal) Kähler potential in the superconformal formalism of [68].”
T-duality and closed string non-commutative (doubled) geometry (2010, background): “• In general, six-dimensional, supersymmetric H-flux backgrounds as well as the non-geometric backgrounds can be best described in terms of so-called generalized geometry, which generalizes the SU(3) group structures of the geometric spaces to background with generalized SU(3) × SU(3) group structur”
Nonperturbative aspects of ABJM theory (2011, result): “We will now confirm this by direct calculation, see [38, 39, 40] for similar considerations.”
The Swampland: Introduction and Review (2019, background): “Rather, it should be a manifold with SU(3) × SU(3) structure group [260].”