Abstract :
As shown by Hořava and Witten, there are gravitational anomalies at the boundaries of M10 × S1/Z2 of 11-dimensional supergravity. They showed that only 10-dimensional vector multiplets belonging to the E8 gauge group can be consistently coupled to this theiry. Thus, the dimensional reduction of this theory should be the low-energy limit of the E8 × E8 heterotic string. Here we assume that M-theory is a theory of supermembranes which includes twisted supermembranes. We show that for a target space M10 × S1/Z2, in the limit in which S1/Z2 in small the effective action is the E8 × E8 heterotic string. We also consider supermembranes on M0 × S1 × S1/Z2 and find the dualities expected from 11-dimensional supergravity on this manifold. We show that the requirements for world-sheet anomaly cancellations at the boundaries of the world-volume action are the same requirements imposed on the Hořava-Witten action.
