Domain Walls and Superpotentials from M Theory on Calabi-Yau Three-Folds

TL;DR

This paper derives the superpotential in M theory compactified on Calabi-Yau three-folds, explores domain wall solutions with wrapped five-branes, and discusses quantum corrections potentially leading to AdS_5 vacua.

Contribution

It provides a direct derivation of the superpotential from eleven-dimensional supergravity and analyzes explicit domain wall solutions with implications for quantum corrections.

Findings

Derived the superpotential from KK reduction of M theory on Calabi-Yau.

Constructed explicit domain wall solutions with wrapped five-branes.

Discussed quantum corrections possibly enabling AdS_5 vacua.

Abstract

Compactification of M theory in the presence of G-fluxes yields N=2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza-Klein reduction of the eleven-dimensional action on a Calabi-Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents five-branes wrapped over holomorphic cycles. This solution has a ``running volume'' and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS_5 vacuum of the 5-dimensional supergravity.