# High Energy Physics - Theory

Abstract: We study the index of $\mathcal{N}=4$ Yang-Mills theory on $S^3\times\mathbb{R}$. We argue that the index should undergo a large $N$ deconfinement phase transition, by computing an upper bound of its temperature.' We compute this bound by optimizing the phases of fugacities. The bound we find has some features analogous to the Hagedorn temperature. We briefly discuss a possible mechanism of the actual deconfinement transition below our bound. Our upper bound is lower than the Hawking-Page transition temperature' of known BPS black holes in the AdS$_5$ dual. We thus expect the existence of new black holes.
 Comments: 18 pages, 3 figures Subjects: High Energy Physics - Theory (hep-th) Report number: SNUTP18-007, KIAS-P18106 Cite as: arXiv:1811.08646 [hep-th] (or arXiv:1811.08646v1 [hep-th] for this version)

## Submission history

From: Seok Kim [view email]
[v1] Wed, 21 Nov 2018 09:21:14 UTC (544 KB)

hep-th
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