Resurgence and Hydrodynamic Attractors in Gauss-Bonnet Holography

Abstract

We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter ${\lambda }_{GB}$. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of $\mathcal{N}=4$ Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of ${\lambda }_{GB}$ considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.

34 pages, 21 figures. Coefficients for the gradient expansion of the energy density provided

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