The M2-M5 Brane System and a Generalized Nahm's Equation

TL;DR

This paper introduces a generalized equation describing M2-branes ending on M5-branes, extending Nahm's equation, with solutions that model fuzzy three-sphere geometries and pass multiple consistency checks.

Contribution

It proposes a new generalized equation for M2-M5 systems, extending Nahm's equation, and explores its solutions and physical implications.

Findings

Constructed solutions using fuzzy three-sphere geometry

Validated the model through consistency checks including energy calculations

Connected the solutions to known D1-D3 and M5-brane configurations

Abstract

We propose an equation that describes M2-branes ending on M5-branes, and which generalizes the description of the D1-D3 system via Nahm's equation. The simplest solution to this equation constructs the transverse geometry in terms of a fuzzy three sphere. We show that the solution passes a number of consistency checks including a consistent reduction to the D1-D3 system, a calculation of the energy of the system, matching to the self-dual string solution in the M5-brane world volume, and a study of simple fluctuations about the ground state configuration. We write down certain terms in the effective action of multiple membranes, which includes a sextic scalar coupling.