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

Abstract

We compute the grand partition function of 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 XXX12 spin chains. We discuss how Hagedorn temperature changes on the complex plane of chemical potentials.