On the supergravity formulation of mirror symmetry in generalized Calabi-Yau manifolds

TL;DR

This paper derives a supergravity framework for mirror symmetry in generalized Calabi-Yau manifolds, showing the effective scalar potential's invariance and its relation to a mirror symmetric superpotential, advancing understanding of flux compactifications.

Contribution

It provides a complete supergravity description of the N=2 scalar potential in flux compactifications on generalized Calabi-Yau manifolds, highlighting mirror symmetry invariance and connecting to a known superpotential.

Findings

Effective potential is mirror symmetric and invariant under specific symplectic groups.

The potential can be expressed in an N=1 form using a mirror symmetric superpotential.

The formulation advances understanding of flux compactifications and mirror symmetry in supergravity.

Abstract

We derive the complete supergravity description of the N=2 scalar potential which realizes a generic flux-compactification on a Calabi-Yau manifold (generalized geometry). The effective potential V_{eff}=V_{(\partial_Z V=0)}$, obtained by integrating out the massive axionic fields of the special quaternionic manifold, is manifestly mirror symmetric, i.e. invariant with respect to {\rm Sp}(2 h_2+2)\times {\rm Sp}(2 h_1+2) and their exchange, being h_1, h_2 the complex dimensions of the underlying special geometries. {\Scr V}_{eff} has a manifestly N=1 form in terms of a mirror symmetric superpotential $W$ proposed, some time ago, by Berglund and Mayr.