A noncommutative M-theory five-brane

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.

Open membranes in a constant C-field background and noncommutative boundary strings

“…When this work was in the process of typing, we learned that another group [16] has also employed the quantization of an open membrane in a C-field background, and they have also investigated the decoupling limit as the open string case. Though their line of thought is different from ours, their results seem to be consistent with ours at least in first order in C. Moreover, their paper has also studied the light-cone coordinate analysis, but their analysis is within the decoupling limit and slightly different from our interests such as membrane regularization related to matrix models.…”

On non-commutative super Yang–Mills

“…In order to realize non-commutativity, a constant 3-form background should be added [37]. However, the 3-form background does not change the geometrical picture.…”

Polyakov Loops for the ABJ Theory

“…A non-commutative string theory on the M5-brane worldvolume has been derived using the action of a single M2-brane [58,59,60]. It would be interesting to analyse the boundary effects for fractional M2-branes using ABJ theory.…”