Generalised geometry and flux vacua

Abstract

This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II N = 1 flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space. This note is a contribution to the proceedings of "The String Theory Universe" workshop in Leuven, 7-11 Sept 2015, to be published by Fortschritte der Physik.

Towards geometric D6-brane model building on non-factorisable toroidal ℤ 4-orbifolds

“…While the above models with a Z 2 × Z 2 subsymmetry allow for rigid fractional three-cycles which, in the open string spectrum, provide gauge groups without brane recombination/splitting moduli in the adjoint representation, it has recently been noticed that (most) twisted complex structure moduli associated to deformations of singularities are in fact stabilised by the existence of D-branes with U (1) symmetries [51,52,50,53]. To further stabilise the dilaton and untwisted complex structure moduli, one usually argues that closed string background NS-NS fluxes (see [54][55][56] for reviews) provide a non-trivial scalar potential, see also [57,58] for attempts to incorporate NS-NS fluxes on the factorisable T 6 Z 4 orbifold and [59] for the factorisable T 6 Z ′ 6 orbifold. However, incorporating a non-trivial NS-NS flux H 3 will in general violate the factorisation into two-tori and instead lead to so-called non-factorisable torus backgrounds [60][61][62].…”

Meromorphic flux compactification

“…Specifically the authors show that for a compactification on a fibered internal space given by a warped product of a four-dimensional torus and a punctured sphere, it is possible to satisfy Bianchi identity and supersymmetric conditions for suitable choices of meromorphic functions depending on the complex coordinates of the sphere. In the same way as F-theory, these flux compactifications with meromorphic functions, dubbed G-theory, gives a geometrical interpretation of the U-duality group (see [19,20]), by replacing the tori by an auxiliary K3.…”