D0-branes on $T^n$ and matrix theory

Abstract

The Hamiltonian describing Matrix theory on T n is identified with the Hamiltonian describing the dynamics of DO-branes on T n in an appropriate weak coupling limit for all n up to 5. New subtleties arise in taking this weak coupling limit for n = 6, since the transverse size of the DO brane system blows up in this limit.This can be attributed to the appearance of extra light states in the theory from wrapped D6 branes.This subtlety is related to the difficulty in finding a Matrix formulation of M-theory on T 6 .During the last year great progress has been made in finding a nonperturbative formulation of M-theory [1-4] and its toroidal compactification [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].This formulation, known as Matrix theory, can be summarized into the following recipe: