Solitons, Superpotentials and Calibrations

TL;DR

This paper explores the generation of superpotentials in Type IIA string theory compactified on Calabi-Yau four-folds, linking BPS solitons to D-branes, proposing a formula, and constructing new supersymmetric vacua.

Contribution

It introduces a general formula for superpotentials induced by fluxes, relates BPS solitons to calibrated D-branes, and constructs new supersymmetric vacua in Calabi-Yau four-fold compactifications.

Findings

Proposed a formula for superpotential from fluxes.

Connected BPS solitons with calibrated D-branes.

Constructed explicit supersymmetric vacua.

Abstract

In this paper we study several issues related to the generation of 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.