Eleven-Dimensional Supergravity on a Manifold with Boundary

TL;DR

This paper analyzes eleven-dimensional supergravity on manifolds with boundary, addressing anomaly cancellation, gauge group determination, and implications for consistent M-theory models.

Contribution

It refines the Green-Schwarz mechanism for anomaly cancellation, uniquely determines boundary gauge groups, and tests the consistency of M-theory with supergravity.

Findings

Gauge group is E8 on each boundary

Fixes gauge coupling in terms of gravitational constant

Provides tests for the consistency of M-theory

Abstract

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 $E_8\times E_8$ 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.