Solitons, superpotentials and calibrations

Abstract

In this paper we study several issues related to the generation of the superpotential induced by background Ramond–Ramond fluxes in compactification of Type IIA string theory on Calabi–Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi–Yau space, we propose a general formula for the superpotential and justify it comparing the supersymmetry conditions in D=2 and D=10 supergravity theories. We also suggest a geometric interpretation to the supersymmetric index in the two-dimensional effective theory in terms of topological invariants of the Calabi–Yau four-fold, and estimate the asymptotic growth of these invariants from BTZ black hole entropy. Finally, we explicitly construct new supersymmetric vacua for Type IIA string theory compactification on a Calabi–Yau four-fold with Ramond–Ramond fluxes.