Abstract
We show that the late-time expansion of the energy density of mathcal{N} = 4 supersymmetric Yang-Mills plasma at infinite coupling undergoing Bjorken flow takes the form of a multi-parameter 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.
Highlights
As the regime of applicability of hydrodynamics [3,4,5,6,7], the role and meaning of the hydrodynamic gradient expansion [8] and attractor behaviour far from equilibrium [9,10,11]
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 multi-parameter transseries
Using the AdS/CFT correspondence we find a gravity solution which supplements the well known large proper-time expansion by exponentiallysuppressed sectors corresponding to quasinormal modes of the AdS black-brane
Summary
Ek is defined to have only the 2k entry non-zero (and equal to 1) These are defined so that the scalar products with A select the corresponding elements, in the sense that ek ·A = Ak, and ek · A = Ak. After substituting our ansatz into eqs. (2.2) to (2.6), the linear independence of Ωn(u) will imply an infinite hierarchy of equations These equations can again be expanded in inverse powers of u to find linear ODEs for the functions h(in), b(in) and d(in). We use residual gauge invariance to set the radial co-ordinate r to keep the horizon fixed at s = 1 at every order. This will amount to choosing h(in)(s = 1) = 0 for all i. By imposing regularity in the bulk and flatness at the boundary for the metric functions we are able to solve for functions fi(n) at each order
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