Two-loop HTL-resummed thermodynamics for N=4 supersymmetric Yang-Mills theory

Abstract

We compute the two-loop hard-thermal-loop (HTL) resummed thermodynamic potential for N=4 supersymmetric Yang-Mills (SYM). Our final result is manifestly gauge-invariant and was renormalized using only simple vacuum energy, gluon mass, scalar mass, and quark mass counter terms. The HTL mass parameters m_D, M_D, and m_q are then determined self-consistently using a variational prescription which results in a set of coupled gap equations. Based on this, we obtain the two-loop HTL-resummed thermodynamic functions of N=4 SYM. We compare our final result with known results obtained in the weak- and strong-coupling limits. We also compare to previously obtained approximately self-consistent HTL resummations and Padé approximants. We find that the two-loop HTL resummed results for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 <= lambda <~ 2 and is in agreement with previous approximately self-consistent HTL resummation results for lambda <~ 6.

arXiv comment38 pages, 7 figures

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Cited by in corpus (8)

• Hydrodynamic dispersion relations at finite coupling
• NNLO HTLpt predictions for the curvature of the QCD phase transition line
• Hard Thermal Loop -- theory and applications
• $\mathcal{N}=4$ supersymmetric Yang-Mills thermodynamics from effective field theory
• $\mathcal{N}=4$ supersymmetric Yang-Mills thermodynamics to order ${\lambda }^2$
• Thermal Emission of Gravitational Waves from Weak to Strong Coupling
• Cosmological constant as a finite temperature effect
• Scheme dependence of two-loop HTLpt-resummed ${\text{SYM}}_{4,4}$ thermodynamics