Superpotentials for Vector Bundle Moduli

TL;DR

This paper introduces a method to explicitly compute non-perturbative superpotentials for vector bundle moduli in heterotic superstrings and M-theory, with applications to stability and cosmology.

Contribution

It provides a general computational method for vector bundle superpotentials applicable to stable, holomorphic bundles over elliptically fibered Calabi-Yau threefolds, including explicit calculations for specific cases.

Findings

Explicit superpotential calculation for SU(3) bundles over specific Calabi-Yau threefolds.

Analysis of the critical points of the superpotential.

Implications for instanton transitions and vacuum stability.

Abstract

We present a method for explicitly computing the non-perturbative superpotentials associated with the vector bundle moduli in heterotic superstrings and M-theory. This method is applicable to any stable, holomorphic vector bundle over an elliptically fibered Calabi-Yau threefold. For specificity, the vector bundle moduli superpotential, for a vector bundle with structure group G=SU(3), generated by a heterotic superstring wrapped once over an isolated curve in a Calabi-Yau threefold with base B=F1, is explicitly calculated. Its locus of critical points is discussed. Superpotentials of vector bundle moduli potentially have important implications for small instanton phase transitions and the vacuum stability and cosmology of superstrings and M-theory.