Type II theories compactified on Calabi–Yau threefolds in the presence of background fluxes

Abstract

Compactifications of type II theories on Calabi-Yau threefolds including electric and magnetic background fluxes are discussed. We derive the bosonic part of the four-dimensional low energy effective action and show that it is a non-canonical N = 2 supergravity which includes a massive two-form. The symplectic invariance of the theory is maintained as long as the flux parameters transform as a symplectic vector and a massive two-form which couples to both electric and magnetic field strengths is present. The mirror symmetry between type IIA and type IIB compactified on mirror manifolds is shown to hold for R-R fluxes at the level of the effective action. We also compactify type IIA in the presence of NS three-form flux but the mirror symmetry in this case remains unclear.

BPS action and superpotential for heterotic string compactifications with fluxes

“…An interesting issue which arises for these solutions is the stabilization of the overall size modulus. In all the known examples of IIB compactifications the resulting effective four-dimensional models were of no-scale type [8,19,23,25,31,35,38] and the overall size modulus remained free even after the introduction of fluxes. This cannot happen in the heterotic compactifications because of the modified Bianchi identity for the three-form [55,46].…”

Calabi-Yau fourfolds with flux and supersymmetry breaking

“…These are the theories that describe the compactifications of eleven-dimensional supergravity on Calabi-Yau fourfolds with background fluxes. We introduce the following split of scalar fields 9) and define the real components ϕ A = ℜφ A ,φ A = ℑφ A . We now assume that the Kähler potential does not depend on theφ A…”

“…9 The starting point is the eleven-dimensional supergravity with (bosonic) Lagrangian [26] e −1 L (11) = 1 2…”

Effects of brane-flux transition on black holes in string theory

“…The negative definite matrix M is defined as in [30]. Note that when the flux H 3 is turned on, the effective theory in four dimensions does not correspond to the usual N = 2 supergravity but to the gauged N = 2 supergravity, see for instance [31].…”

“…The presence of the NS-NS flux H 3 in the internal manifold induces a change in the effective action. The resulting action of the gauged N = 2 supergravity in four dimensions is given in [30], where the N = 2 supersymmetry is maintained by the presence of a positive definite scalar potential. To summarize, both fluxes, RR and NS-NS, must be turned on and moreover, they must be supported on the same cycle Π 3 .…”