Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes

Understand

We show that the Nahm equation which describes a fuzzy D3-brane in the presence of a B-field can be derived as a boundary condition of the F1-strings ending on the D3-brane, and that the modifications of the original Nahm equation by a B-field can be understood in terms of the noncommutative geometry of the D3-brane.

• Naturally this is consistent with the alternative derivation by quantising the open strings in the B-field background.
• We then consider a configuration of multiple M2-branes ending on an M5-brane with a constant 3-form C-field.
• By analogy with the case of strings ending on a D3-brane with a constant B-field, one can expect that this system can be described in terms of the boundary of the M2-branes moving within a certain kind of quantum geometry on the M5-brane worldvolume.