Matrix strings in a B-field

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 [1]. We then discuss the coupling of a B-field to the Matrix model of Mtheory. 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 Teichmüller 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.

The superstring Hagedorn temperature in a pp-wave background

“…Recently, there has been some discussion on the Hagedorn behavior of pp-wave strings [5,6] also in discrete light cone quantization [7]. It is well known that when string theories are placed in a background electric NS B field or in a metric, the Hagedorn temperature depends on the parameters of the background [52,53,54]. Here we shall find that also the RR flux (1.5) felt by a string in the pp-wave metric modifies the Hagedorn temperature.…”

Two-dimensional gauge theories of the symmetric group Sn and branched n-coverings of Riemann surfaces in the large-n limit

“…Along this line, it was recently proposed in [13] that the phase transition we find is a close analogue of the Hagedorn phase transition in Matrix String Theory described in Refs. [14][15][16][17][18].…”

The target space depenedence of the Hagedorn temperature

“…This is another limit of string theory which is described by a gauge theory, the matrix model, which does not involve gravity. We found in [17] that the B-field couples to the thermodynamic partition function of both free type II superstring theory and the matrix string. Indeed, the Hagedorn temperature there is also modified by a factor of √ 1 − B 2 , with no reference to the light-cone radius R. This poses a subtlety for discrete light-cone quantization of strings.…”