Abstract
By using holographic methods, the radii of convergence of the hydrodynamic shear and sound dispersion relations were previously computed in the mathcal{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.
Highlights
In the hydrodynamic regime, quantum field theory is expected to contain collective excitations such as sound waves [1, 2]
We have determined the dependence on the coupling of the radii of convergence of the shear and sound hydrodynamic dispersion relations in the strongly coupled N = 4 SU(Nc) Yang-Mills theory (SYM) theory
Limiting ourselves to the results obtained using the standard perturbation theory only, the coupling constant dependence of the radii in the shear and sound channels is given by eqs. (1.7), (1.8), respectively. These perturbative results suggest that the radii of convergence increase with the ‘t Hooft coupling decreasing from its infinite value
Summary
Quantum field theory is expected to contain collective excitations such as sound waves [1, 2]. This analysis is done perturbatively and non-perturbatively by using the “resummed” version of the first-order theory. The recipe for computing the two-point retarded correlators from dual gravity [31] implies that the spectral curve P (q2, w) = 0 is determined by the boundary value Z(u = 0, q2, w) of the solution Z(u, q2, w) to the bulk equations of motion for the fluctuations coupled to the relevant conserved current: P (q2, w) = Z(u = 0, q2, w) = 0 [4, 5]. We continue working in the limit Nc → ∞, and extend the approach of refs. [4, 5] to bulk gravity theories with higher derivative terms, i.e., to the domain of large but finite ‘t Hooft coupling
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