A note on supersymmetric Yang-Mills thermodynamics

Abstract

The thermodynamics of supersymmetric Yang-Mills theories is studied by computing the two-loop correction to the canonical free energy and to the equation of state for theories with 16, 8 and 4 supercharges in any dimension $4\le d\le 10$, and in two dimensions at finite volume. In the four-dimensional case we also evaluate the first non-analytic contribution in the 't Hooft coupling to the free energy, arising from the resummation of ring diagrams. To conclude, we discuss some applications to the study of the Hagedorn transition in string theory in the context of Matrix strings and speculate on the possible physical meaning of the transition.

19 pages, harvmac, epsf. 1 figure included. Minor changes: typos corrected; references, a footonote and a note added

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• String Thermodynamics in D-Brane Backgrounds
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• M-Theory and Stringy Corrections to Anti-de Sitter Black Holes and Conformal Field Theories
• String Corrections to the Hawking-Page Phase Transition
• Black Holes and Five-brane Thermodynamics
• High Temperature Limit of the N= 2 Matrix Model
• Matrix Strings, Compactification Scales and Hagedorn Transition
• Non-perturbative Thermodynamics in Matrix String Theory

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• Perturbative Thermal QCD: Formalism and Applications
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• Debye screening in strongly coupled N=4 supersymmetric Yang-Mills plasma
• Static Potential in N=4 Supersymmetric Yang-Mills Theory
• The Free Energy of N=4 Super-Yang-Mills and the AdS/CFT Correspondence
• New Effects in Gauge Theory from pp-wave Superstrings
• Thermodynamics of Large-N Super Yang-Mills Theory and AdS/CFT Correspondence
• Hard thermal loops and the entropy of supersymmetric Yang-Mills theories
• Some Implications of Perturbative Approach to AdS/CFT Correspondence
• QCD and String Theory
• Hagedorn inflation of D-branes
• Transverse momentum broadening and collinear radiation at NLO in the $\mathcal{N}=4$ SYM plasma
• Color-kinematics duality and dimensional reduction for graviton emission in Regge limit
• Higher derivative corrections to near-extremal black holes in type IIB supergravity
• Two-loop HTL-resummed thermodynamics for N=4 supersymmetric Yang-Mills theory
• $\mathcal{N}=4$ supersymmetric Yang-Mills thermodynamics from effective field theory
• Thermodynamics of SU(2) N=2 supersymmetric Yang-Mills theory
• On thermodynamics of N=6 superconformal Chern-Simons theory
• Hagedorn Inflation: Open Strings on Branes Can Drive Inflation
• $\mathcal{N}=4$ supersymmetric Yang-Mills thermodynamics to order ${\lambda }^2$
• Temperature of D3-branes off extremality
• $N^2$ entropy of 4D N=4 SYM
• Gauge-String Dualities and Some Applications
• Free Energy of ABJM Theory
• Scheme dependence of two-loop HTLpt-resummed ${\text{SYM}}_{4,4}$ thermodynamics