A Noncommutative M-Theory Five-brane

TL;DR

This paper explores the impact of a constant C-field on M-theory five-branes, revealing a noncommutative loop space structure through open membrane quantization in a specific decoupling limit.

Contribution

It introduces a non-degenerate open membrane metric and demonstrates the emergence of a noncommutative loop space analogous to D-brane noncommutativity.

Findings

Open membrane boundary quantization yields noncommutative loop space.

Defined a non-degenerate open membrane metric in the decoupling limit.

Established a functional analogue of noncommutative geometry for five-branes.

Abstract

We investigate, in a certain decoupling limit, the effect of having a constant C-field on the M-theory five-brane using an open membrane probe. We define an open membrane metric for the five-brane that remains non-degenerate in the limit. The canonical quantisation of the open membrane boundary leads to a noncommutative loop space which is a functional analogue of the noncommutative geometry that occurs for D-branes.