Type II Theories Compactified on Calabi-Yau Threefolds in the Presence of Background Fluxes

TL;DR

This paper derives the four-dimensional effective action for type II string theories compactified on Calabi-Yau threefolds with background fluxes, revealing a non-canonical N=2 supergravity with symplectic invariance and exploring mirror symmetry.

Contribution

It presents the explicit form of the effective action including electric and magnetic fluxes, demonstrating symplectic invariance and mirror symmetry for R-R fluxes in type II compactifications.

Findings

Effective action includes a massive two-form coupled to electric and magnetic fields.

Mirror symmetry holds for R-R fluxes at the effective action level.

NS flux case mirror symmetry remains unresolved.

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.