Two-Loop String Theory on Null Compactifications

TL;DR

This paper calculates two-loop free energy contributions in null compactified string theories, providing insights into their moduli space and implications for orbifold CFTs and matrix string theory.

Contribution

It introduces an explicit parametrization of the moduli space of worldsheets in null compactifications, advancing the understanding of higher-loop effects in string theory.

Findings

Explicit two-loop free energy calculations for various string types.

Description of arithmetic and physical properties of instanton sums.

Discussion of applications to orbifold CFTs and matrix string theory.

Abstract

We compute the two-loop contributions to the free energy in the null compactification of perturbative string theory at finite temperature. The cases of bosonic, Type II and heterotic strings are all treated. The calculation exploits an explicit reductive parametrization of the moduli space of infinite-momentum frame string worldsheets in terms of branched cover instantons. Various arithmetic and physical properties of the instanton sums are described. Applications to symmetric product orbifold conformal field theories and to the matrix string theory conjecture are also briefly discussed.