Abstract
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 6th 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.
Highlights
While a gravity dual replaces a path integral description of a strongly interacting field theory with a set of nonlinear, partial differential equations, i.e. Einstein’s equations, Einstein’s equations are still difficult to solve
In cases of high symmetry, the equations can sometimes be solved analytically, but the lack of symmetry in strongly time dependent and out-of-equilibrium states typically necessitates solving Einstein’s equations numerically. (See [3] for a review of numerical relativity techniques applied to holography.) solving Einstein’s equations in situations with little or no symmetry is a common problem in general relativity, for example, in studying the emission of gravitational waves from black-hole mergers
Our analysis demonstrates that the 1/D expansion is asymptotic and gives insight into the early time physics, which is missing from the standard hydrodynamic approach
Summary
Bjorken flow is the solution of relativistic hydrodynamics under the assumption that the fluid motion is invariant under boosts along one of the space directions of the system, x. After some trivial thermodynamic manipulations, eq (2.5) may be written as ̇ n By comparing this expression with the conservation equation (2.2), boost invariant flow consistent with a truncation to second order in inverse normalized gradients is given by the ratio. Since the hydrodynamic equation (2.8) truncates the gradient corrections at second order, higher-powers in the u-expansion in the microscopic theory are sensitive to additional gradient corrections and they differ, in principle from those extracted from the power series analysis of eq (2.8). To close this section and for future notational convenience, let us briefly discuss how to go beyond second order hydrodynamics to an arbitrary order in the gradient expansion In this case, we can present the conservation equation (2.8) in the form ̇ n.
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