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We show that the Polyakov loop approaches its asymptotic value at high temperatures {\it from below} in any strongly-coupled gauge theory at large $N_c$ with a dual supergravity description.
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One can see that by writing the 10 dimensional action in the Einstein frame, which leads to an overall factor of l P l a n c k 8 ∼ N c 2 l_{Planck}^{8}\sim N_{c}^{2} (after defining R = 1 R=1 ). See, for instance, J. M. Maldacena, arXiv:hep-th/0309246
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For a recent study of the Polyakov loop in perturbation theory see Y. Burnier, M. Laine and M. Vepsalainen, JHEP 1001
2010
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J. Noronha, Phys. Rev. D 81
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