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Gauge Field Dynamics In and Out of Equilibrium
(INT Program March 5 - April 13, 2012)

Reported by G. Aarts, G.D. Moore, M. Laine
  Date posted April 20, 2012

The many-body physics of relativistic non-Abelian gauge theories plays an important role in current heavy ion collision experiments, in the astrophysics of compact stars, as well as in cosmology. Within the program, the methods available for studying such systems were discussed on a broad spectrum, ranging from analytic effective field theory techniques, through numerical lattice Monte Carlo simulations, all the way to string-theory inspired dualities. Specific focal points were: scrutinizing recent advances in the non-perturbative study of systems with a finite baryon density; the issue of how fast thermalization can take place; as well as mapping the status of perturbative and non-perturbative particle production rate computations, both with and without resonance enhancement.


  • QCD phase diagram at finite density
  • As is well known, the Boltzmann weight in the QCD path integral is complex at non-zero chemical potential, which poses a formidable challenge for practical simulations. There are ongoing efforts to evade this problem, via the use of imaginary chemical potential, the strong coupling expansion, or the density of states method. A relatively recent alternative uses complex Langevin dynamics. The program brought together various experts in the field, and allowed for intense discussions on the pros and cons of various approaches. It is hoped that studies in simplified systems, some of them of academic nature but others actually relevant for strongly interacting systems, help to suggest avenues for progress.

  • Thermalization
  • Given some values for thermodynamic potentials and transport coefficients, the macroscopic evolution of a system and the propagation of various probe particles can be studied via hydrodynamics. One focus of the meeting was on the values of these transport coefficients and on how close to "ideal" the hydrodynamic evolution really is. Another focus was on the route to equilibrium in a heavy ion collision, from the initially very nonequilibrium initial conditions. We had a review of the picture in strong coupling, and a vigorous discussion of some competing scenarios and open questions in the case that the energy density is so high that weak coupling methods should apply. The way that over-occupied plasmas approach equilibrium was at least partly clarified. In particular it became clear during the meeting that a Bose-Einstein condensate does not play a major role in these dynamics, and is probably in any case not a well defined notion.

  • Towards systematic determination of transport coefficients and spectral functions
  • The dynamical properties of a many-body system, particularly the rates at which various types of particles are being produced, are encoded in various gauge-invariant spectral functions and their zero-frequency limits, known as transport coefficients. It would be of utmost importance to develop controlled non-perturbative methods for the determination of these quantities, starting from Euclidean correlators computed via Monte Carlo simulations. Moreover, effective field theory techniques or computations in idealized but related theories may help to develop a generic understanding of the qualitative shape of the spectral functions. The meeting had some intensive discussions about the strengths and limitations of various methods for the analytic continuation of Euclidean data to obtain spectral functions. In addition applications to QCD problems of current importance, particularly heavy quark correlators, as well as to cosmology, in which case resummed perturbative computations could suffice, were considered.