M2-branes stretching 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.