Why matrix theory works for oddly shaped membranes - art. no. 086003

We give a simple proof of why there is a matrix theory approximation for a membrane shaped like an arbitrary Riemann surface. As corollaries, we show that noncompact membranes cannot be approximated by matrices, and that the Poisson algebra on any compact phase space is U(infinity). The matrix appro ximation does not appear to work properly in theories such as type IIB stri ng theory or bosonic membrane theory where there is no conserved 3-form cha rge to which the membranes couple.