Open multiple M2-branes I: quantum geometry of the M5-brane in a C-field

Abstract

We show that the Nahm equation and the Basu–Harvey equation which provide the fuzzy funnel description can be understood as the boundary condition of the F1-strings or M2-branes probing the intersecting branes system. In particular the noncommutative geometry of a D3-brane in the presence of a constant B-field can be identified with a constant shift in the B-field modified Nahm equation. Since the C-field modified Basu–Harvey equation can be derived from the known behaviour of the system in the Bion description, in order for this modification to be consistent with the boundary condition of the M2-branes, we derive a new type of quantum geometry on the M5-brane worldvolume. Unlike the D-brane case, this is naturally expressed in terms of a relation between a 3-bracket of the M5-brane worldvolume coordinates and the C-field.