Matrix theory interpretation of discrete light cone quantization string worldsheets

We study the null compactification of type-IIA string perturbation theory a t finite temperature. We prove a theorem about Riemann surfaces establishin g that the moduli spaces of infinite-momentum-frame superstring worldsheets are identical to those of branched-cover instantons in the matrix-string m odel conjectured to describe M theory. This means that the identification o f string degrees of freedom in the matrix model proposed by Dijkgraaf, Verl inde, and Verlinde is correct and that its natural generalization produces the moduli space of Riemann surfaces at all orders in the genus expansion.