Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-04-12
JHEP 0107:004,2001
Physics
High Energy Physics
High Energy Physics - Theory
55 pages, one figure in text, some references added and misprints corrected
Scientific paper
10.1088/1126-6708/2001/07/004
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.
Grignani Gianluca
Orselli Marta
Semenoff Gordon W.
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