Two-loop HTL-resummed thermodynamics for $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

Du, Qianqian; Strickland, Michael; Tantary, Ubaid; Zhang, Ben-Wei

doi:10.1007/jhep09(2020)038

Cited by 16 publications

(31 citation statements)

References 53 publications

(121 reference statements)

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“…In the context of finite temperature QCD, such resummations have been carried out through O(λ 3 log λ) [1][2][3][4][5] and reorganizations of perturbation theory based on hard thermal loop perturbation theory and the Φ-derivable approach have shown that one can extend the radius of convergence of weak-coupling treatments to intermediate couplings g ∼ 2 [34][35][36][37][38][39][40]. We note that such perturbative reorganizations have also been carried out to two-loop order in SYM 4,4 [41,42].…”

Section: Jhep08(2021)064mentioning

confidence: 99%

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$$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

Strickland

Tantary

2021

J. High Energ. Phys.

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We calculate the resummed perturbative free energy of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM4,4) 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 SYM4,4 ring diagrams. Non-analytic terms at $$ \mathcal{O} $$ O (λ3/2) and $$ \mathcal{O} $$ O (λ2 log λ) are generated by dressing the A0 and scalar propagators. The gauge-field Debye mass mD and the scalar thermal mass MD are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM4,4 to $$ \mathcal{O} $$ O (λ2). We compare 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-Nc strong-coupling result. Our results suggest that the $$ \mathcal{O} $$ O (λ2) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

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Section: Jhep08(2021)064mentioning

confidence: 99%

“…result [42] by setting the gluonic transverse self-energy to zero and the longitudinal selfenergy to m 2 D . The coefficient b 0 is defined as…”

Section: Jhep08(2021)064mentioning

confidence: 99%

$$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

Strickland

Tantary

2021

J. High Energ. Phys.

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“…Shift the field ζ →ζ +ζ (17) whereζ,ζ denote the fluctuation field and background field, respectively. Since we are interested in the potential as opposed to the action, the background fieldζ can be treated as a constant.…”

Section: Flat Spacetime Analysismentioning

confidence: 99%

“…(Reviews can be found in [10][11][12][13][14].) For a high temperature, say, that of the QCD era, a well-known example is the 'Linde problem' [15], which has been an active topic of research; see [16] [17] and references therein. An effective field theory approach combined with lattice computation was proposed to deal with the problem [18].…”

Section: Introductionmentioning

confidence: 99%

Cosmological Constant as a Finite Temperature Effect

Park¹

2021

Preprint

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The cosmological constant problem is examined by taking an Einstein--scalar with a Higgs-type potential and scrutinizing the infrared structure induced by finite temperature effects. A variant optimal perturbation theory is implemented in the recently proposed quantum-gravitational framework. The optimized renormalized mass, i.e., the renormalized mass determined by the variant optimal perturbation theory, of the scalar field turns out to be on the order of the temperature. This shifts the cosmological constant problem to compatibility of the consequent perturbative analysis. The compatibility is guaranteed essentially by renormalization group invariance of physical quantities. We point out the resummation behind the invariance.

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“…kinetic) regime in the same theory. This interpolation, even for simplest theories such as CFTs considered at finite temperature, is not fully understood [16,33,36,[48][49][50][51][52]. Admittedly, relying -even only qualitatively -on the non-perturbative treatment in models arising as truncations of a perturbative expansion may seem to be unwarranted [34].…”

Section: Non-perturbative Quasinormal Modes and Singular Perturbation Theorymentioning

confidence: 99%

Hydrodynamic dispersion relations at finite coupling

Grozdanov

Starinets²,

Tadić

2021

J. High Energ. Phys.

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By using holographic methods, the radii of convergence of the hydrodynamic shear and sound dispersion relations were previously computed in the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory at infinite ’t Hooft coupling and infinite number of colours. Here, we extend this analysis to the domain of large but finite ’t Hooft coupling. To leading order in the perturbative expansion, we find that the radii grow with increasing inverse coupling, contrary to naive expectations. However, when the equations of motion are solved using a qualitative non-perturbative resummation, the dependence on the coupling becomes piecewise continuous and the initial growth is followed by a decrease. The piecewise nature of the dependence is related to the dynamics of branch point singularities of the energy-momentum tensor finite-temperature two-point functions in the complex plane of spatial momentum squared. We repeat the study using the Einstein-Gauss-Bonnet gravity as a model where the equations can be solved fully non-perturbatively, and find the expected decrease of the radii of convergence with the effective inverse coupling which is also piecewise continuous. Finally, we provide arguments in favour of the non-perturbative approach and show that the presence of non-perturbative modes in the quasinormal spectrum can be indirectly inferred from the analysis of perturbative critical points.

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Two-loop HTL-resummed thermodynamics for $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

Cited by 16 publications

References 53 publications

$$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

$$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

Cosmological Constant as a Finite Temperature Effect

Hydrodynamic dispersion relations at finite coupling

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