Membrane and non-commutativity Original Research Article

We analyse the dynamics of an open membrane, both for the free case and when it is coupled to a background three-form, whose boundary is attached to p-branes. The role of boundary conditions and constraints in the Nambu–Goto and Polyakov formulations is studied. The low-energy approximation that effectively reduces the membrane to an open string is examined in detail. Non-commutative features of the boundary string coordinates, where the cylindrical membrane is attached to the Dp-branes, are revealed by algebraic consistency arguments and not by treating boundary conditions as primary constraints, as is usually done. The exact form of the non-commutative algebra is obtained in the low-energy limit.