Logarithmic Corrections to the Equation of State in the SU(2)xSU(2) Nambu - Jona-Lasinio Model

We present results from a Monte Carlo simulation of the Nambu - Jona-Lasinio model, with continuous SU(2)xSU(2) chiral symmetry, in four Euclidean dimensions. Different model equations of state, corresponding to different theoretical scenarios, are tested against the order parameter data. The results are sensitive to necessary assumptions about the shape and extent of the scaling region. Our best fits favour a trivial scenario in which the logarithmic corrections are qualitatively similar to those predicted by the large N_f approximation. This is supported by a separate analysis of finite volume corrections for data taken directly in the chiral limit.Comment: 37 pages LaTeX (RevTeX) including 12 .eps 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

Lattice Gauge Theory and (Quasi)-Conformal Technicolor

QCD with 2 flavours of massless colour-sextet quarks is studied as a theory which might exhibit a range of scales over which the running coupling constant evolves very slowly (walks). We simulate lattice QCD with 2 flavours of sextet staggered quarks to determine whether walks, or if it has an infrared fixed point, making it a conformal field theory. Our initial simulations are performed at finite temperatures $T=1/N_ta$ ($N_t=4$ and $N_t=6$), which allows us to identify the scales of confinement and chiral-symmetry breaking from the deconfinement and chiral-symmetry restoring transitions. Unlike QCD with fundamental quarks, these two transitions appear to be well-separated. The change in coupling constants at these transitions between the two different temporal extents $N_t$, is consistent with these being finite temperature transitions for an asymptotically free theory, which favours walking behaviour. In the deconfined phase, the Wilson Line shows a 3-state signal. Between the confinement and chiral transitions, there is an additional transition where the states with Wilson Lines oriented in the directions of the complex cube roots of unity disorder into a state with a negative Wilson Line.Comment: 7 pages Latex, 3 postscript figures. Talk presented by DKS at SCGT09, Nagoya, Japa