The chiral extension of Quantum Chromodynamics (XQCD) adds to the standard lattice action explicit pseudoscalar meson fields for the chiral condensates. With this action, it is feasible to do simulations at the chiral limit with zero mass Goldstone modes. We review the arguments for why this is expected to be in the same universality class as the traditional action. We present preliminary results on convergence of XQCD for naive fermions and on the methodology for introducing counter terms to restore chiral symmetry for Wilson fermions.

We investigate the Maximally Abelian (MA) Projection for a single SU (2) instanton in continuum gauge theory. We find that there is a class of solutions to the differential MA gauge condition with circular monopole loops of radius R centered on the instanton of width ρ. However, the MA gauge fixing functional G decreases monotonically as R/ρ → 0. Its global minimum is the instanton in the singular gauge. We point out that interactions with nearby anti-instantons are likely to excite these monopole loops.

We consider a particular 4 state spin system composed of two Ising spins ( s x , σ x ) with independent hopping parameters κ 1 , κ 2 , coupled by a bilinear Yukawa term, ys x σ x . The Yukawa term is solely responsible for breaking the global Z 2 × Z 2 symmetry down to Z 2 . This model is intended as an illustration of general coupled Higgs system where scalars can arise both as composite and elementary excitations. For the Ising example in 2d, we give convincing numerical evidence of the universality of the two spin system with the one spin Ising model, by Monte Carlo simulations and finite scaling analysis . We also show that as we approach the phase transition, universality arises by a separation of low mass spin waves from an extra set of spin waves with an energy gap that diverges as the correlations length diverges.