Higher Order Corrections to the Hagedorn Temperature at Strong Coupling

Abstract

We propose a general formula for higher order corrections to the value of the Hagedorn temperature of a class of holographic confining gauge theories in the strong coupling expansion. Inspired by recent proposals in the literature, the formula combines the sigma-model string expansion with an effective approach. In particular, it includes the sigma-model contributions to the Hagedorn temperature at next-to-next-to leading order, which are computed in full generality. For $\mathcal{N}=4$ SYM on $S^3$ our result agrees with numerical field theory estimates with excellent precision. We use the general formula to predict the value of the Hagedorn temperature for ABJM on $S^2$ and for the dual of purely RR global $Ad{S}_3$.

13 pages. V2: added clarifications, some typos fixed. V3: minor improvements

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Cited by in corpus (5)

• Hagedorn temperature in holography: world-sheet and effective approaches
• On the asymptotic density of states in solvable models of strings
• Vacuum configuration of winding superstrings from non-standard semiclassical quantization
• Holographic Hagedorn Temperature: Strong Coupling, Flavor and $\theta$-angle Effects
• Hawking-Page transition on a spin chain