Five-Brane Thresholds and Membrane Instantons in Four-Dimensional Heterotic M-Theory

TL;DR

This paper studies how five-branes in heterotic M-theory influence the four-dimensional effective supergravity, revealing non-perturbative effects from membrane instantons and their impact on vacuum structure.

Contribution

It derives the interactions of the interval modulus from five-brane anomaly-cancelling terms and constructs their supergravity description, highlighting non-perturbative superpotential effects.

Findings

Derived five-brane induced interaction terms in supergravity.

Identified membrane instanton effects generating superpotentials.

Discussed implications for vacuum structure in heterotic M-theory.

Abstract

The effective four-dimensional supergravity of M-theory compactified on the orbifold S^1/Z_2 and a Calabi-Yau threefold includes in general moduli supermultiplets describing massless modes of five-branes. For each brane, one of these fields corresponds to fluctuations along the interval. The five-brane also leads to modifications of the anomaly-cancelling terms in the eleven-dimensional theory, including gauge contributions located on their world-volumes. We obtain the interactions of the brane "interval modulus" predicted by these five-brane-induced anomaly-cancelling terms and we construct their effective supergravity description. In the condensed phase, these interaction terms generate an effective non-perturbative superpotential which can also be interpreted as instanton effects of open membranes stretching between five-branes and the S^1/Z_2 fixed hyperplanes. Aspects of the vacuum structure of the effective supergravity are also briefly discussed.