Twisted bundle on quantum torus and BPS states in matrix theory

Following the recent work of Connes, Douglas and Schwarz, we study the M(atrix) model compactified on a torus with a background of the three-form field. This model is given by a super Yang-Mills theory on a quantum torus. To consider twisted gauge field configurations, we construct twisted U(n) bundles on the quantum torus as a deformation of its classical counterpart. By properly taking into account membranes winding around the light-cone direction, we derive from the M(atrix) model the BPS spectrum which respects the full SL(2,Z) x SL(2,Z) U-duality in M theory. (C) 1998 Elsevier Science B.V. All rights reserved.