FINITE-TEMPERATURE MATRIX-THEORY

We present a way in which the Lorentz invariant canonical partition fu nction for Matrix theory as a light-cone formulation of M-theory can b e computed. We explicitly show how, when the eleventh dimension is dec ompactified, the N = 1 eleven-dimensional SUGRA partition function app ears. We also provide a high temperature expansion which captures some structure of the canonical partition function when interactions among st D-particles are turned on. The connection with the semi-classical c omputations thermalizing the open superstrings attached to a D-particl e is also clarified through a Born-Oppenheimer approximation. Some ide as about how Matrix theory would describe the complementary degrees of freedom of the massless content of eleven-dimensional SUGRA are discu ssed. Comments on possible connections to black hole physics are also made, (C) 1998 Elsevier Science B.V.