We use effective kinetic theory, accurate at weak coupling, to simulate the preequilibrium evolution of transverse energy and flow perturbations in heavy-ion collisions. We provide a Green function which propagates the initial perturbations to the energymomentum tensor at a time when hydrodynamics becomes applicable. With this map, the complete pre-thermal evolution from saturated nuclei to hydrodynamics can be modelled in a perturbatively controlled way.

CERN

Liam Keegan

Norway

Aleksi Kurkela

United States

Aleksas Mazeliauskas

Derek Teaney

Initial conditions for hydrodynamics from weakly coupled pre-equilibrium evolution

We present a direct comparison studying equilibration through kinetic theory at weak coupling and through holography at strong coupling in the same set-up. The set-up starts with a homogeneous thermal state, which then smoothly transitions through an out-of-equilibrium phase to an expanding system undergoing boost-invariant flow. This first apples-to-apples comparison of equilibration provides a benchmark for similar equilibration processes in heavy-ion collisions, where the equilibration mechanism is still under debate. We find that results at weak and strong coupling can be smoothly connected by simple, empirical power-laws for the viscosity, equilibration time and entropy production of the system.

Paul Romatschke

Wilke Schee

Finland

Yan Zhu

Weak and strong coupling equilibration in nonabelian gauge theories

In this work we consider the SU(N) gauge theory with two Dirac fermions in the adjoint representation, in the limit of large N. In this limit the infinite-volume physics of this model can be studied by means of the corresponding twisted reduced model defined on a single site lattice. Making use of this strategy we study the reduced model for various values of N up to 289. By analyzing the eigenvalue distribution of the adjoint Dirac operator we test the conformality of the theory and extract the corresponding mass anomalous dimension.

Spain

Margarita García Pérez

Antonio González-Arroyo

Japan

Masanori Okawa

Mass anomalous dimension of adjoint QCD at large N from twisted volume reduction

We investigate Monte Carlo updating algorithms for simulating SU( N ) YangMills fields on a single-site lattice, such as for the Twisted Eguchi-Kawai model (TEK). We show that performing only over-relaxation (OR) updates of the gauge links is a valid simulation algorithm for the Fabricius and Haan formulation of this model, and that this decorrelates observables faster than using heat-bath updates. We consider two different methods of implementing the OR update: either updating the whole SU( N ) matrix at once, or iterating through SU(2) subgroups of the SU( N ) matrix, we find the same critical exponent in both cases, and only a slight difference between the two.

Margarita Pérez

Alberto Ramos

A comparison of updating algorithms for large N reduced models

We measure the running of the SU(∞) ’t Hooft coupling by performing a step scaling analysis of the Twisted Eguchi-Kawai (TEK) model, the SU( N ) gauge theory on a single site lattice with twisted boundary conditions. The computation relies on the conjecture that finite volume effects for SU(N) gauge theories defined on a 4-dimensional twisted torus are controlled by an effective size parameter l ˜ = l N $$ \tilde{l}=l\sqrt{N} $$ , with l the torus period. We set the scale for the running coupling in terms of l ˜ $$ \tilde{l} $$ and use the gradient flow to define a renormalized ’t Hooft coupling λ l ˜ $$ \lambda \left(\tilde{l}\right) $$ . In the TEK model, this idea allows the determination of the running of the coupling through a step scaling procedure that uses the rank of the group as a size parameter. The continuum renormalized coupling constant is extracted in the zero lattice spacing limit, which in the TEK model corresponds to the large N limit taken at fixed value of λ l ˜ $$ \lambda \left(\tilde{l}\right) $$ . The coupling constant is thus expected to coincide with that of the ordinary pure gauge theory at N = ∞. The idea is shown to work and permits us to follow the evolution of the coupling over a wide range of scales. At weak coupling we find a remarkable agreement with the perturbative two-loop formula for the running coupling.

The SU(∞) twisted gradient flow running coupling