Matrix Theory Interpretation of DLCQ String Worldsheets

TL;DR

This paper proves a theorem linking superstring worldsheet moduli spaces to matrix-string instantons, confirming the matrix model's validity in describing M-theory at all genus levels.

Contribution

It establishes a rigorous mathematical connection between superstring worldsheets and matrix-string instantons, supporting the matrix model's role in M-theory.

Findings

Moduli spaces of superstring worldsheets are identical to those of matrix-string instantons.

The matrix model correctly captures string degrees of freedom.

The correspondence holds at all orders in the genus expansion.

Abstract

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