Refined counting of necklaces in one-loop mathcal{N}=4 SYM

Abstract

We compute the grand partition function of mathcal{N}=4 SYM at one-loop in the SU(2) sector with general chemical potentials, extending the results of Pólya’s theorem. We make use of finite group theory, applicable to all orders of perturbative 1/Nc expansion. We show that only the planar terms contribute to the grand partition function, which is therefore equal to the grand partition function of an ensemble of {mathrm{XXX}}_{frac{1}{2}} spin chains. We discuss how Hagedorn temperature changes on the complex plane of chemical potentials.