COUPLING-CONSTANT DEPENDENCE IN THE THERMODYNAMICS OF NU=4 SUPERSYMMETRIC YANG-MILLS THEORY

The free energy of the maximally supersymmetric SU(N) gauge theory at temperature T is expected to scale, in the large-N limit, as (NT4)-T-2 times a function of the 't Hooft coupling, f(g(YM)(2)N). In the stron g coupling limit the free energy has been deduced from the near-extrem al 3-brane geometry, and its normalization has turned out to be 3/4 ti mes that found in the weak coupling limit. In this paper we calculate the leading correction to this result in inverse powers of the couplin g, which originates from the R-4 terms in the tree-level effective act ion of type IIB string theory. The correction to 3/4 is positive and o f order (g(YM)(2)N)(-3/2). Thus, f(g(YM)(2)N) increases as the 't Hoof t coupling is decreased, in accordance with the expectation that it sh ould be approaching 1 in the weak coupling limit. We also discuss simi lar corrections for other conformal theories describing coincident bra nes. In particular, we suggest that the coupling independence of the n ear extremal entropy for D1-branes bound to D5-branes is related to th e vanishing of the Weyl tensor of AdS(3) x S-3. (C) 1998 Published by Elsevier Science B.V.