Matrix string partition functions

We evaluate quasi-classically the Ramond partition function of Euclidean D=10 U(N) super-Yang–Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasi-classical expressions reproduce exactly the recently obtained expression for the partition function of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasi-classical calculation might be exact.