Five-brane thresholds and membrane instantons in four-dimensional heterotic M-theory

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. (c) 2005 Elsevier B.V. All rights reserved.