Eleven-dimensional supergravity on a manifold with boundary

In this paper, we present a systematic analysis of eleven-dimensional supergravity on a manifold with boundary, which is believed to be relevant to the strong coupling limit of the E 8 × E 8 heterotic string. Gauge and gravitational anomalies enter at a very early stage, and require a refinement of the standard Green-Schwarz mechanism for their cancellation. This uniquely determines the gauge group to be a copy of E 8 for each boundary component, fixes the gauge coupling constant in terms of the gravitational constant, and leads to several striking new tests of the hypothesis that there is a consistent quantum M-theory with eleven-dimensional supergravity as its low-energy limit.