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

We study weakly coupled SU(N)N=4 super-Yang-Mills theory on R×S3 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 Pólya'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 δlnTH=+λ/8π2.