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/N c 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.
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ArXiv ePrint: 1703.05798
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Suzuki, R. Refined counting of necklaces in one-loop \( \mathcal{N}=4 \) SYM. J. High Energ. Phys. 2017, 55 (2017). https://doi.org/10.1007/JHEP06(2017)055
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DOI: https://doi.org/10.1007/JHEP06(2017)055