Open Supermembranes Coupled to M-Theory Five-Branes

TL;DR

This work analyzes open supermembranes in eleven dimensions ending on M‑theory five‑branes, focusing on reparametrisation anomalies arising from chiral boundary fermions. The authors compute the boundary anomaly and demonstrate its cancellation by a classical coupling on the membrane–five‑brane world‑volume, provided relations among the membrane tension $T_3$, five‑brane tension $T_6$, and the eleven‑dimensional gravitational constant $ abla^{2}$ (consistent with Dirac quantization) hold. The anomaly calculation relies on the modified Bianchi identities for the self‑dual two‑form on the five‑brane and yields a single physical scale through Dirac quantization. These results establish the quantum consistency of open membranes in M‑theory, illuminate connections to Horava–Witten configurations, and relate to reductions to Type II‑A branes in various limits.

Abstract

We consider open supermembranes in eleven dimensions in the presence of closed M-Theory five-branes. It has been shown that, in a flat space-time, the world-volume action is kappa invariant and preserves a fraction of the eleven dimensional supersymmetries if the boundaries of the membranes lie on the five-branes. We calculate the reparametrisation anomalies due to the chiral fermions on the boundaries of the membrane and examine their cancellation mechanism. We show that these anomalies cancel with the aid of a classical term in the world-volume action, provided that the tensions of the five-brane and the membrane are related to the eleven dimensional gravitational constant in a way already noticed in M-Theory.