Shear Viscosity at Infinite Coupling: A Field Theory Calculation.

I derive an exact integral expression for the ratio of shear viscosity over entropy density η/s for the massless (critical) O(N) model at large N with quartic interactions. The calculation is set up and performed entirely from the field theory side using a nonperturbative resummation scheme that captures all contributions to leading order in large N. In 2+1d, η/s is evaluated numerically at all values of the coupling. For infinite coupling, I find (η/s)≃0.42(1)×N. I show that this strong coupling result for the viscosity is universal for a large class of interacting bosonic O(N) models.

Erratum: Finite-Temperature Conformal Field Theory Results for All Couplings: O(N) Model in 2+1 Dimensions [Phys. Rev. Lett. 122, 231603 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.122.231603.

Finite-Temperature Conformal Field Theory Results for All Couplings: O(N) Model in 2+1 Dimensions.

A famous example of gauge-gravity duality is the result that the entropy density of the strongly coupled N=4 supersymmetric Yang-Mills theory in four dimensions for large N is exactly 3/4 of the Stefan-Boltzmann limit. In this work, I revisit the massless O(N) model in 2+1 dimensions, which is analytically solvable at a finite-temperature T for all couplings λ in the large N limit. I find that the entropy density monotonically decreases from the Stefan-Boltzmann limit at λ=0 to exactly 4/5 of the Stefan-Boltzmann limit at λ=∞. Calculating the retarded energy-momentum tensor correlator in the scalar channel at λ=∞, I find that it has two logarithmic branch cuts originating at ω=±4Tln(1+sqrt[5]/2) but no singularities in the whole complex frequency plane. I show that the ratio 4/5 and the location of the branch points both are universal within a large class of bosonic conformal field theories in 2+1 dimensions.

Fractional Degrees of Freedom at Infinite Coupling in Large N_{f} QED in 2+1 Dimensions.

I consider quantum electrodynamics with many electrons in 2+1 space-time dimensions at finite temperature. The relevant dimensionless interaction parameter for this theory is the fine structure constant divided by the temperature. The theory is solvable at any value of the coupling, in particular for very weak (high temperature) and infinitely strong coupling (corresponding to the zero temperature limit). Concentrating on the photon, each of its physical degrees of freedom at infinite coupling only contributes half of the free-theory value to the entropy. These fractional degrees of freedom are reminiscent of what has been observed in other strongly coupled systems (such as N=4 supersymmetric Yang-Mills theory), and bear similarity to the fractional quantum Hall effect, potentially suggesting connections between these phenomena. The results found for (2+1)-dimensional QED are fully consistent with the expectations from particle-vortex duality.

Next-to-Next-to-Next-to-Leading Order Pressure of Cold Quark Matter: Leading Logarithm.

At high baryon chemical potential µ_{B}, the equation of state of QCD allows a weak-coupling expansion in the QCD coupling α_{s}. The result is currently known up to and including the full next-to-next-to-leading order α_{s}^{2}. Starting at this order, the computations are complicated by the modification of particle propagation in a dense medium, which necessitates nonperturbative treatment of the scale α_{s}^{1/2}µ_{B}. We apply a hard-thermal-loop scheme for capturing the contributions of this scale to the weak-coupling expansion, and we use it to determine the leading-logarithm contribution to next-to-next-to-next-to-leading order: α_{s}^{3}ln^{2}α_{s}. This result is the first improvement to the equation of state of massless cold quark matter in 40 years. The new term is negligibly small and thus significantly increases our confidence in the applicability of the weak-coupling expansion.

Relativistic Fluid Dynamics Far From Local Equilibrium.

Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this gradient series diverges, but can be Borel resummed, giving rise to a hydrodynamic attractor solution which is well defined even for large gradients. Arbitrary initial data quickly approaches this attractor via nonhydrodynamic mode decay. This suggests the existence of a new theory of far-from-equilibrium fluid dynamics. In this Letter, the framework of fluid dynamics far from local equilibrium for a conformal system is introduced, and the hydrodynamic attractor solutions for resummed Baier-Romatschke-Son-Starinets-Stephanov theory, kinetic theory in the relaxation time approximation, and strongly coupled N=4 super Yang-Mills theory are identified for a system undergoing Bjorken flow.

Nonspherically Symmetric Collapse in Asymptotically AdS Spacetimes.

We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of nonspherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time.

Nonhydrodynamic Transport in Trapped Unitary Fermi Gases.

Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of nonhydrodynamic modes. We review nonhydrodynamic modes in kinetic theory and gauge-gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data we find hints of nonhydrodynamic modes in cold Fermi gases in two and three dimensions.

Simulation of black hole collisions in asymptotically Anti-de Sitter spacetimes.

We present results from the evolution of spacetimes that describe the merger of asymptotically global anti-de Sitter black holes in 5D with an SO(3) symmetry. Prompt scalar field collapse provides us with a mechanism for producing distinct trapped regions on the initial slice, associated with black holes initially at rest. We evolve these black holes towards a merger, and follow the subsequent ring down. The boundary stress tensor of the dual conformal field theory is conformally related to a stress tensor in Minkowski space that inherits an axial symmetry from the bulk SO(3). We compare this boundary stress tensor to its hydrodynamic counterpart with viscous corrections of up to second order, and compare the conformally related stress tensor to ideal hydrodynamic simulations in Minkowski space, initialized at various time slices of the boundary data. Our findings reveal far-from-hydrodynamic behavior at early times, with a transition to ideal hydrodynamics at late times.

Fully dynamical simulation of central nuclear collisions.

We present a fully dynamical simulation of central nuclear collisions around midrapidity at LHC energies. Unlike previous treatments, we simulate all phases of the collision, including the equilibration of the system. For the simulation, we use numerical relativity solutions to anti-de Sitter space/conformal field theory for the preequilibrium stage, viscous hydrodynamics for the plasma equilibrium stage, and kinetic theory for the low-density hadronic stage. Our preequilibrium stage provides initial conditions for hydrodynamics, resulting in sizable radial flow. The resulting light particle spectra reproduce the measurements from the ALICE experiment at all transverse momenta.

Viscous hydrodynamic predictions for nuclear collisions at the LHC.

Hydrodynamic simulations are used to make predictions for the integrated elliptic flow coefficient v2 in square root(s) = 5.5 TeV lead-lead and square root(s) = 14 TeV proton-proton collisions at the LHC. We predict a 10% increase in v2 from RHIC to Pb+Pb at LHC, and v2 approximately 0 in p+p collisions unless eta/s<0.08.

Viscosity information from relativistic nuclear collisions: how perfect is the fluid observed at RHIC?

Relativistic viscous hydrodynamic fits to Brookhaven Relativistic Heavy Ion Collider data on the centrality dependence of multiplicity, transverse, and elliptic flow for square root s = 200 GeV Au+Au collisions are presented. For standard (Glauber-type) initial conditions, while data on the integrated elliptic flow coefficient v(2) are consistent with a ratio of viscosity over entropy density up to eta/s approximately 0.16, data on minimum bias v(2) seem to favor a much smaller viscosity over entropy ratio, below the bound from the anti-de Sitter conformal field theory conjecture. Some caveats on this result are discussed.

Collective non-Abelian instabilities in a melting color glass condensate.

We present first results for (3 + 1)D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a non-Abelian Weibel instability leading soft modes to grow with proper time tau as exp(gamma square root(g2 mu tau)), where g2 mu is a scale arising from the saturation of gluons in the nuclear wave function. The scale for the growth rate gamma is set by a plasmon mass, defined as omega(pl) = kappa0 square root(g2 mu/tau)), generated dynamically in the collision. We compare the numerical ratio gamma/kappa0 to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.

Plasma instabilities in an anisotropically expanding geometry.

We study (3+1)D kinetic (Boltzmann-Vlasov) equations for relativistic plasma particles in a one dimensionally expanding geometry motivated by ultrarelativistic heavy-ion collisions. We set up local equations in terms of Yang-Mills potentials and auxiliary fields that allow simulations of hard- (expanding-) loop dynamics on a lattice. We determine numerically the evolution of plasma instabilities in the linear (Abelian) regime and also derive their late-time behavior analytically, which is consistent with recent numerical results on the evolution of the so-called melting color-glass condensate. We also find a significant delay in the onset of growth of plasma instabilities which are triggered by small rapidity fluctuations, even when the initial state is highly anisotropic.

Hard-loop dynamics of non-Abelian plasma instabilities.

Non-Abelian plasma instabilities may be responsible for the fast apparent quark-gluon thermalization in relativistic heavy-ion collisions if their exponential growth is not hindered by nonlinearities. We study numerically the real-time evolution of instabilities in an anisotropic non-Abelian plasma with an SU(2) gauge group in the hard-loop approximation. We find exponential growth of non-Abelian plasma instabilities both in the linear and in the strongly nonlinear regimes, with only a brief phase of subexponential behavior in between.