Matrix strings in a B-field

We study the discrete light-cone quantization (DLCQ) of closed strings in t he background of Minkowski space-time and a constant Neveu-Schwarz B-field. For the Bosonic string, we identify the B-dependent part of the thermodyna mic free energy to all orders in string perturbation theory. For every genu s, B appears in a constraint in the path integral which restricts the world -sheet geometries to those which are branched covers of a certain torus. Th is is the extension of a previous result where the B-field was absent [1]. We then discuss the coupling of a B-field to the Matrix model of M-theory. We show that, when we consider this theory at finite temperature and in a f inite B-field, the Matrix variables are functions which live on a torus wit h the same Teichmuller parameter as the one that we identified in string th eory. We show explicitly that the thermodynamic partition function of the M atrix string model in the limit of free strings reproduces the genus 1 ther modynamic partition function of type-IIA string. This is strong evidence th at the Matrix model can reproduce perturbative string theory. We also find an interesting behavior of the Hagedorn temperature.