City Research Online

Abstract

We consider planar N = 4 super Yang-Mills at finite temperature with chemical potentials that couple either to the R-charges or the spins of the operators. We find expressions for the Hagedorn temperatures at both zero coupling by explicitly counting states, and at strong coupling using the string theory dual. We then apply the quantum spectral curve (QSC) to this problem, which adds additional twists to the Q-functions. For a single chemical potential μ coupled to one of the R-charges, we find the analytic weak-coupling Hagedorn temperature to one-loop order for any value of μ, and to two-loop order for μ = 1/2. We then solve the QSC numerically, showing that at strong coupling there is good agreement with the string theory prediction to order 1/λ1/4. This provides further evidence for a recent conjecture of Harmark for the form of the world-sheet zero-point shift. We also use the QSC to find the analytic one-loop correction to the Hagedorn temperature with non-zero chemical potentials coupled to the spins.

Publication Type:	Article
Additional Information:	© The Authors This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Publisher Keywords:	AdS-CFT Correspondence, Integrable Field Theories, Nonperturbative Effects
Subjects:	Q Science Q Science > QC Physics
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics
SWORD Depositor:	Symplectic Administrator

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