A note on the M2-M5 brane system and fuzzy spheres

TL;DR

This paper explores fuzzy geometry approaches to describing membranes ending on fivebranes, focusing on the Basu-Harvey equation, non-associative algebra, and the resulting degrees of freedom in fuzzy funnel solutions.

Contribution

It analyzes the relation between the Basu-Harvey and Nahm equations and investigates the implications of non-associative algebra for fuzzy three-spheres.

Findings

Fuzzy funnel solutions have Q^{3/2} degrees of freedom.

Non-associative algebra affects the structure of fuzzy spheres.

Connections between membrane and fivebrane descriptions are clarified.

Abstract

This note covers various aspects of recent attempts to describe membranes ending on fivebranes using fuzzy geometry. In particular, we examine the Basu-Harvey equation and its relation to the Nahm equation as well as the consequences of using a non-associative algebra for the fuzzy three-sphere. This produces the tantalising result that the fuzzy funnel solution corresponding to Q coincident membranes ending on a five-brane has $Q^{3/2}$ degrees of freedom.