Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation

Consistent formulations of relativistic viscous hydrodynamics involve short lived modes, leading to asymptotic rather than convergent gradient expansions. In this Letter we consider the Mueller-Israel-Stewart theory applied to a longitudinally expanding quark-gluon plasma system and identify hydrodynamics as a universal attractor without invoking the gradient expansion. We give strong evidence for the existence of this attractor and then show that it can be recovered from the divergent gradient expansion by Borel summation. This requires careful accounting for the short-lived modes which leads to an intricate mathematical structure known from the theory of resurgence.Comment: Presentation improved, typos fixed; roughly matches the published versio

On the gravity dual of strongly coupled charged plasma

Locally asymptotically AdS solutions of Einstein equations coupled with a vector field with a weakly curved boundary metric are found within the fluid-gravity gradient expansion up to second order in gradients. This geometry is dual to 1+3 dimensional hydrodynamics with a conserved current in a weakly curved background. The causal structure of the bulk geometry is determined and it is shown that the black brane singularity is shielded by an event horizon

Hydrodynamization in kinetic theory: Transient modes and the gradient expansion

We explore the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a vanishing radius of convergence due to the presence of a transient (nonhydrodynamic) mode, in a way similar to results obtained earlier in strongly-coupled gauge theories. This suggests that the mechanism by which hydrodynamic behaviour emerges is the same, which we further corroborate by a novel comparison between solutions of different weakly and strongly coupled models. However, in contrast with other known cases, we find that not all the singularities of the analytic continuation of the Borel transform of the gradient expansion correspond to transient excitations of the microscopic system: some of them reflect analytic properties of the kinetic equation when the proper time is continued to complex values.Comment: 6 pages, 2 figures, v2: author added, major rewrite, mysterious off real axis singularities in the Borel plane explained (!), see also arXiv:1802.08225 [nucl-th] by Heller and Svensson; v3: references added, minor improvements in the text, first 426 terms from Eq. (8) included in the submission; v4: title changed, matches published versio

Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma

Relativistic hydrodynamics simulations of quark-gluon plasma play a pivotal role in our understanding of heavy ion collisions at RHIC and LHC. They are based on a phenomenological description due to Mueller, Israel, Stewart (MIS) and others, which incorporates viscous effects and ensures a well-posed initial value problem. Focusing on the case of conformal plasma we propose a generalization which includes, in addition, the dynamics of the least damped far-from-equilibrium degree of freedom found in strongly coupled plasmas through the AdS/CFT correspondence. We formulate new evolution equations for general flows and then test them in the case of N=4 super Yang-Mills plasma by comparing their solutions alongside solutions of MIS theory with numerical computations of isotropization and boost-invariant flow based on holography. In these tests the new equations reproduce the results of MIS theory when initialized close to the hydrodynamic stage of evolution, but give a more accurate description of the dynamics when initial conditions are set in the pre-equilibrium regime.Comment: Minor improvements; references adde

Supergravity Instantons and the Universal Hypermultiplet

The effective action of N=2 supersymmetric 5-dimensional supergravity arising from compactifications of M-theory on Calabi-Yau threefolds receives non-perturbative corrections from wrapped Euclidean membranes and fivebranes. These contributions can be interpreted as instanton corrections in the 5 dimensional field theory. Focusing on the universal hypermultiplet, a solution of this type is presented and the instanton action is calculated, generalizing previous results involving membrane instantons. The instanton action is not a sum of membrane and fivebrane contributions: it has the form reminiscent of non-threshold bound states.Comment: 16 pages, harvmac(b), no figures, reference added, minor changes, version to appear in JHE

Entropy currents from holography in hydrodynamics with charge

The holographic interpretation of the hydrodynamic entropy current is developed for the case of hydrodynamics with a conserved charge. This is carried out within a framework developed in earlier work, which showed how to associate entropy currents with horizons in the dual geometry. The entropy current defined by the event horizon in the dual bulk geometry is calculated. It is also shown that to second order in the gradient expansion the dual geometry possesses a unique Weyl-invariant apparent horizon which also defines an admissable entropy current. At first order both currents coincide with the result obtained on the basis of a purely hydrodynamic analysis.Comment: Additional comments and references; version appearing in JHEP. arXiv admin note: text overlap with arXiv:1102.288