Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

Abstract

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.

Holography and hydrodynamics with weakly broken symmetries

“…To show how the MIS equations arise from a dual gravitational description, we focus on the Einstein-Gauss-Bonnet theory [53,54,103,104], which is a useful holographic toy model for analyzing thermal field theories at intermediate coupling strengths. The crucial feature of the theory, and of other higher-derivative theories, is the emergence of quasinormal modes with a purely relaxing, imaginary dispersion relation ω(k) [51,54,105]. As was demonstrated in [51,54], these modes reproduce many expected spectral properties of thermal theories in transition from strong, towards weak coupling.…”

The complex life of hydrodynamic modes

“…The main focus of ref. [27] was on the possibility of recovering the full spectrum from the hydrodynamic derivative expansion, similar to recovering the non-hydrodynamic modes from asymptotic series via Borel resummation and resurgence [17,18,25]. The quasinormal spectrum in the holographic models with finite temperature T and non-vanishing chemical potential µ such as the one considered in ref.…”

“…As already mentioned in ref. [8] in the context of the discussion of the "unreasonable effectiveness" of hydrodynamics as an effective theory, many previous studies have reported the divergence of the derivative expansion in relativistic hydrodynamics [15,17,18,18,25]. Possibly, the asymptotic nature of the expansion appearing in those publications should be viewed as a reflection of the singular nature of the state about which this expansion is performed, rather than a generic property of the hydrodynamic gradient expansion itself.…”

The large proper-time expansion of Yang-Mills plasma as a resurgent transseries

“…[46][47][48]) and calculated numerically to high orders in Refs. [8,16]. We adopt the Eddington-Finkelstein (EF) coordinate system which implements the symmetries of Bjorken flow with the following ansatz [3,[49][50][51]…”

“…These coefficients ε (n) k have been included with this submission for the sectors Φ n with n = 0, e 1 , e 2 , 2e 1 , (e 1 +e 1 ), along with their corresponding exponential weights A i and characteristic exponents β n . For the hydrodynamic sector Φ 0 coefficients for the hydrodynamic expansion were taken from [16].…”