M2-branes stretching between M5-branes

TL;DR

This paper presents exact solutions to a generalized BPS equation describing M2-branes stretching between M5-branes, providing a consistency check for a recent conjecture in M-theory brane dynamics.

Contribution

It offers explicit solutions to a proposed BPS equation for M2-M5 brane configurations, supporting the conjecture and enhancing understanding of multiple M-brane dynamics.

Findings

Exact solutions to the generalized Nahm's equation for M2-M5 systems.

Support for the Basu-Harvey conjecture through consistency checks.

Insights into the boundary conditions of M2-branes between M5-branes.

Abstract

A generalization of Nahm's equation has been recently conjectured by Basu and Harvey to be the BPS condition describing the bound state of a stack of M2-branes ending on an M5-brane. In this note exact solutions are presented for the proposed BPS equation - which is from the point of view of the M2-brane world-volume dynamics - with boundary conditions appropriate for M2-branes stretching between two M5-branes. Unfortunately, since the action for multiple M5-branes or for multiple coincident M2-branes is not known, one can only resort to consistency checks of the proposal instead of a direct comparison of the M2 and M5 world-volume point of views. The existence of our solutions should be seen as such a consistency check of the conjecture, and also as a source of new insight into the dynamics of multiple M2 and M5-branes.