Hydrodynamic dispersion relations at finite coupling

Abstract

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.

A holographic superfluid symphony

“…dynamics throughout the phase diagram following the recent studies [50,[108][109][110][111][112][113][114][115][116][117][118][119] in other holographic models.…”

The breakdown of magneto-hydrodynamics near AdS2 fixed point and energy diffusion bound

“…As in other perturbative expansions, one may ask about the convergence of the hydrodynamic expansion such as "does the hydrodynamic expansion indeed converge?" In JHEP02(2022)006 recent years, regarding this question, the breakdown of hydrodynamics has been investigated in [2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Breakdown of hydrodynamics from holographic pole collision

“…It was proposed in [3][4][5][6] that, by viewing the hydrodynamic mode as complex spectral curve in C 2 of complexified frequency and momentum, the convergence radii (k eq , ω eq ) of the hydrodynamic dispersion series is set by the absolute value of the complex momentum and complex frequency where the hydrodynamic pole collides with the first non-hydrodynamic gapped pole, namely "pole collision". Along this line, the convergence of hydrodynamic dispersion series has been investigated using kinetic theory in [10], using field theory in [11,12] and using holographic duality in [13][14][15][16][17][18][19][20].…”

“…Certainly the scale at which hydrodynamics breaks down depends on the details of the microscopic dynamics. The convergence radii are different for hydrodynamics of field theories with different 't Hooft couplings or gauge couplings [11,12,14,17]. Meanwhile, the origins of the first non-hydrodynamic modes are different for different systems, for example, it could be a slow mode due to symmetry breaking [24][25][26] or an infra-red (IR) mode for hydrodynamics at low temperature [15].…”

“…Note that monotonic behavior for the convergence radius as functions of coupling has been found in [11] using the experimental data for fluids. There are also studies in [12,17] showing the non-monotonic dependence of the coupling strength in the theory. It is interesting to understand the dependence of hydrodynamic convergence on the coupling constant better.…”