Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory Original Research Article

The free energy of the maximally supersymmetric SU(N) gauge theory at temperature T is expected to scale, in the large-N limit, as N2T4 times a function of the ʹt Hooft coupling, f (gYM2N). In the strong coupling limit the free energy has been deduced from the near-extremal 3-brane geometry, and its normalization has turned out to be 34 times that found in the weak coupling limit. In this paper we calculate the leading correction to this result in inverse powers of the coupling, which originates from the R4 terms in the tree-level effective action of type IIB string theory. The correction to 34 is positive and of order (gYM2N)−32. Thus, f(gYM2N) increases as the ʹt Hooft coupling is decreased, in accordance with the expectation that is should be approaching 1 in the weak coupling limit. We also discuss similar corrections for other conformal theories describing coincident branes. In particular, we suggest that the coupling independence of the near extremal entropy for D1-branes bound to D5-branes is related to the vanishing of the Weyl tensor of AdS3 × S3.