No abstract

We have studied lattice QCD with an additional, irrelevant 4-fermion interaction having a U (1) × U (1) chiral symmetry, at finite temperatures. Adding this 4-fermion term allowed us to work at zero quark mass, which would have otherwise been impossible. The theory with 2 massless staggered quark flavours appears to have a first order finite temperature phase transition at N t = 4 for the value of 4-fermion coupling we have chosen, in contrast to what is expected for 2-flavour QCD. The pion screening mass is seen to vanish below this transition, only to become massive and degenerate with the σ (f 0 ) above this transition where the chiral symmetry is restored, as is seen by the vanishing of the chiral condensate.

QCD with two flavours of massless colour-sextet quarks is considered as a model for conformal/walking Technicolor. If this theory possess an infrared fixed point, as indicated by 2-loop perturbation theory, it is a conformal(unparticle) field theory.If, on the other hand, a chiral condensate forms on the weak-coupling side of this would-be fixed point, the theory remains confining. The only difference between such a theory and regular QCD is that there is a range of momentum scales over which the coupling constant runs very slowly (walks). In this first analysis, we simulate the lattice version of QCD with two flavours of staggered quarks at finite temperatures on lattices of temporal extent N t = 4 and 6. The deconfinement and chiral-symmetry restoration couplings give us a measure of the scales associated with confinement and chiral-symmetry breaking. We find that, in contrast to what is seen with fundamental quarks, these transition couplings are very different. β = 6/g 2 for each of these transitions increases significantly from N t = 4 and N t = 6 as expected for the finite temperature transitions of an asymptotically-free theory. This suggests a walking rather than a conformal behaviour, in contrast to what is observed with Wilson quarks. In contrast to what is found for fundamental quarks, the deconfined phase exhibits states in which the Polyakov loop is oriented in the directions of all three cube roots of unity. At very weak coupling the states with complex Polyakov loops undergo a transition to a state with a real, negative Polyakov loop.2

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 Lüscher-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.