We use gauge/gravity duality to study the dynamics of strongly coupled gauge theories undergoing boost invariant expansion in an arbitrary number of space-time dimensions (D). By keeping the scale of the late-time energy density fixed, we explore the infinite-D limit and study the first few corrections to this expansion. In agreement with other studies, we find that the large-D dynamics are controlled by hydrodynamics and we use our computation to constrain the leading large-D dependence of a certain combination of transport coefficients up to 6 th order in gradients. Going beyond late time physics, we discuss how non-hydrodynamic modes appear in the large-D expansion in the form of a trans-series in D, identical to the non-perturbative contributions to the gradient expansion. We discuss the consequence of this trans-series in the non-convergence of the large-D expansion.

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 λ 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 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 λ GB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.

We show that the late-time expansion of the energy density of N = 4 supersymmetric Yang-Mills plasma at infinite coupling undergoing Bjorken flow takes the form of a multiparameter transseries. Using the AdS/CFT correspondence we find a gravity solution which supplements the well known large proper-time expansion by exponentially-suppressed sectors corresponding to quasinormal modes of the AdS black-brane. The full solution also requires the presence of further sectors which have a natural interpretation as couplings between these modes. The exponentially-suppressed sectors represent nonhydrodynamic contributions to the energy density of the plasma. We use resurgence techniques on the resulting transseries to show that all the information encoded in the nonhydrodynamic sectors can be recovered from the original hydrodynamic gradient expansion.

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