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N = 4 supersymmetric Yang-Mills thermodynamics to order λ^2

Aug 11, 2022, 2:15 PM
Oral report TeV物理和超出标准模型新物理 Parallel Session IX (1):TeV and BSM Physics


Dr Qianqian Du (Guangxi Normal University)


We calculate the resummed perturbative free energy of N = 4 supersymmetric Yang-Mills in four spacetime dimensions $SYM_{4,4}$ through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over $SYM_{4,4}$ ring diagrams. Non-analytic terms at $\mathcal{O}(λ^{3/2})$ and $\mathcal{O}(λ^{2} log λ)$ are generated by dressing the $A_{0}$ and scalar propagators. The gauge-field Debye mass $m_{D}$ and the scalar thermal mass $M_{D}$ are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of $SYM_{4,4}$ to $\mathcal{O}(λ^{2})$.


By comparing our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-$N_{c}$ strong-coupling result. Our results suggest that the $\mathcal{O}(λ^{2})$ weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

Primary author

Dr Qianqian Du (Guangxi Normal University)


Prof. Michael Strickland (Kent State University) Dr Ubaid Tantary (Kent State University)

Presentation materials