Matrix strings in a B-field

TL;DR

This paper investigates the effects of a constant B-field on the thermodynamics of closed strings in light-cone quantization, extending previous results and connecting to Matrix theory, with implications for understanding string perturbation and the Hagedorn temperature.

Contribution

It extends the analysis of string thermodynamics to include a B-field, showing how it constrains world-sheet geometries and linking these results to the Matrix model of M-theory at finite temperature.

Findings

B-field modifies the string free energy and world-sheet constraints.

Matrix model variables at finite B-field are defined on a torus with a specific Teichmüller parameter.

The free string limit of the Matrix model reproduces genus 1 string thermodynamics.

Abstract

We study the discrete light-cone quantization (DLCQ) of closed strings in the background of Minkowski space-time and a constant Neveu-Schwarz $B$-field. For the Bosonic string, we identify the $B$-dependent part of the thermodynamic free energy to all orders in string perturbation theory. For every genus, $B$ appears in a constraint in the path integral which restricts the world-sheet geometries to those which are branched covers of a certain torus. This is the extension of a previous result where the $B$-field was absent \cite{Grignani:2000zm}. 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 finite $B$-field, the Matrix variables are functions which live on a torus with the same Teichm\"uller parameter as the one that we identified in string theory. We show explicitly that the thermodynamic partition function of the Matrix string model in the limit of free strings reproduces the genus 1 thermodynamic partition function of type IIA string. This is strong evidence that the Matrix model can reproduce perturbative string theory. We also find an interesting behavior of the Hagedorn temperature.