Open supermembranes in eleven dimensions

TL;DR

This paper investigates open supermembranes in eleven dimensions, demonstrating their symmetry properties, anomaly cancellation mechanisms, and their relation to M-theory through boundary conditions and topological defects.

Contribution

It introduces the conditions under which open supermembranes exhibit symmetries and anomalies, linking boundary dynamics to M-theory consistency.

Findings

World-volume action is kappa-symmetric in flat spacetime.

Anomalies on boundaries require boundary current algebras.

Membrane tension relates to gravitational constant via Green-Schwarz mechanism.

Abstract

We consider open supermembranes in an eleven dimensional background. We show that, in a flat space-time, the world-volume action is kappa-symmetric and has global space-time supersymmetry if space-time has even dimensional topological defects where the membrane can end. An example of such topological defects is provided by the space-time with boundaries considered by Horava and Witten. In that case the world-volume action has reparametrisation anomalies whose cancellation requires the inclusion of a current algebra on the boundaries of the membrane. The role of kappa-anomalies in a general background is discussed. The tension of the membrane is related to the eleven dimensional gravitational constant with the aid of the Green-Schwarz mechanism allowing a consistency check of M-theory.