Equilibrium Thermodynamics of Lattice QCD

Lattice QCD allows us to simulate QCD at non-zero temperature and/or densities. Such equilibrium thermodynamics calculations are relevant to the physics of relativistic heavy-ion collisions. I give a brief review of the field with emphasis on our work.Comment: 15 pages, 9 figures. Talk presented at SCGT06, Nagoya, Japan. Version 2 includes minor modifications to reference work not covered in version

Quantization and simulation of Born-Infeld non-linear electrodynamics on a lattice

Born-Infeld non-linear electrodynamics arises naturally as a field theory description of the dynamics of strings and branes. Most analyses of this theory have been limited to studying it as a classical field theory. We quantize this theory on a Euclidean 4-dimensional space-time lattice and determine its properties using Monte-Carlo simulations. The electromagnetic field around a static point charge is measured using Luscher-Weisz methods to overcome the sign problem associated with the introduction of this charge. The D field appears identical to that of Maxwell QED. However, the E field is enhanced by quantum fluctuations, while still showing the short distance screening observed in the classical theory. In addition, whereas for the classical theory, the screening increases without bound as the non-linearity increases, the quantum theory approaches a limiting conformal field theory.Comment: 24 pages, 10 figures. Latex with postscript figure

Complex Langevin Simulations of QCD at Finite Density -- Progress Report

We simulate lattice QCD at finite quark-number chemical potential to study nuclear matter, using the complex Langevin equation (CLE). The CLE is used because the fermion determinant is complex so that standard methods relying on importance sampling fail. Adaptive methods and gauge-cooling are used to prevent runaway solutions. Even then, the CLE is not guaranteed to give correct results. We are therefore performing extensive testing to determine under what, if any, conditions we can achieve reliable results. Our earlier simulations at $\beta=6/g^2=5.6$, $m=0.025$ on a $12^4$ lattice reproduced the expected phase structure but failed in the details. Our current simulations at $\beta=5.7$ on a $16^4$ lattice fail in similar ways while showing some improvement. We are therefore moving to even weaker couplings to see if the CLE might produce the correct results in the continuum (weak-coupling) limit, or, if it still fails, whether it might reproduce the results of the phase-quenched theory. We also discuss action (and other dynamics) modifications which might improve the performance of the CLE.Comment: Talk presented at Lattice 2017, Granada, Spain and submitted to proceedings. 8 pages, 4 figure