PANIC2021 Conference

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

5 Sept 2021, 15:44

18m

Online

Talk Hot and dense matter physics - QGP and heavy ion collisions Hot and dense matter physics - QGP and heavy ion collisions

Speaker

Ubaid Tantary (Kent State University, Kent Ohio, USA.)

Description

We calculate the resummed perturbative free energy of $\mathcal{N}=4$ supersymmetric Yang-Mills in four spacetime dimensions through second order in the 't Hooft coupling $\lambda$ 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 $\mathcal{N}=4$ supersymmetric Yang-Mills ring diagrams. Non-analytic terms at $\mathcal{O}({\lambda }^{3/2})$ and $\mathcal{O}({\lambda }^2\log \lambda )$ 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 $\mathcal{N}=4$ supersymmetric Yang-Mills to $\mathcal{O}({\lambda }^2)$. We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Pad\'{e} approximant that interpolates between the weak-coupling result and the large-$N_c$ strong-coupling result. Our results suggest that the $\mathcal{O}({\lambda }^2)$ weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for $0\le \lambda \le 2$.
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Presentation materials

Panic Slides.pptx

Panic_Slides_UTantary.pdf