From supermembrane to super-Yang-Mills theory

We derive (p+1)-dimensional ( p=1, 2) maximally supersymmetric U(N) Yang-Mills theory from the wrapped supermembrane on R×T in the light-cone gauge by using the matrix regularization. The elements of the matrices in the super-Yang-Mills theory are given by the Fourier coefficients in the supermembrane theory. Although our approach never refers to both D-branes and superstring dualities, we obtain the relations which exactly represent T-duality.