On the Thermodynamics of Large N Noncommutative Super Yang-Mills Theory

We study the thermodynamics of the large N noncommutative super Yang-Mills theory in the strong 't Hooft coupling limit in the spirit of AdS/CFT correspondence. It has already been noticed that some thermodynamic quantities of near-extremal D3-branes with NS B fields, which are dual gravity configurations of the noncommutative ${\cal N}$=4 super Yang-Mills theory, are the same as those without B fields. In this paper, (1) we examine the $\alpha'^3 R^4$ corrections to the free energy and find that the part of the tree-level contribution remains unchanged, but the one-loop and the non-perturbative D-instanton corrections are suppressed, compared to the ordinary case. (2) We consider the thermodynamics of a bound state probe consisting of D3-branes and D-strings in the near-extremal D3-brane background with B field, and find the thermodynamics of the probe is the same as that of a D3-brane probe in the D3-brane background without B field. (3) The stress-energy tensor of the noncommutative super Yang-Mills theory is calculated via the AdS/CFT correspondence. It is found that the tensor is not isotropic and its trace does not vanish, which confirms that the super Yang-Mills is not conformal even in four dimensions due to the noncommutative nature of space. Our results render further evidence for the argument that the large N noncommutative and ordinary super Yang-Mills theories are equivalent not only in the weak coupling limit, but also in the strong coupling limit.