The one-loop partition function of N=4 super-Yang-Mills theory on R x S3

We study weakly coupled SU(N) N = 4 super-Yang-Mills theory on R x S-3 at infinite N, which has interesting thermodynamics, including a Hagedorn transition, even at zero Yang-Mills coupling. We calculate the exact one-loop partition function below the Hagedorn temperature. Our calculation employs the representation of the one-loop dilatation operator as a spin chain Hamiltonian acting on neighboring sites and a generalization of Polya's counting of necklaces (gauge-invariant operators) to include necklaces with a 'pendant' (an operator which acts on neighboring beads). We find that the one-loop correction to the Hagedorn temperature is delta lnT(H) = +lambda/8 pi(2). (c) 2005 Elsevier B.V. All rights reserved.