Chiral Extension of Lattice Gauge Theory

Two approaches are presented to coupling explicit Goldstone modes to $N_f$ flavors of massless quarks preserving exact $SU(N_f) \times SU(N_f)$ chiral symmetry on the lattice. The first approach is a generalization a chiral extension to QCD (aka XQCD) proposed by Brower, Shen and Tan consistent with the Ginsparg-Wilson relation. The second approach based on the Callan,Coleman, Wess and Zumino coset construction has a real determinant atzero quark axial coupling, $g_A = 0$.Comment: Lattice2003 3 pages, 1 figur

Multigrid for propagators of staggered fermions in four-dimensional SU(2)SU(2) gauge fields

Multigrid (MG) methods for the computation of propagators of staggered fermions in non-Abelian gauge fields are discussed. MG could work in principle in arbitrarily disordered systems. The practical variational MG methods tested so far with a ``Laplacian choice'' for the restriction operator are not competitive with the conjugate gradient algorithm on lattices up to $18^4$. Numerical results are presented for propagators in $SU(2)$ gauge fields.Comment: 4 pages, 3 figures (one LaTeX-figure, two figures appended as encapsulated ps files); Contribution to LATTICE '92, requires espcrc2.st

Generalized simplicial chiral models

Using the auxiliary field representation of the simplicial chiral models on a (d-1)-dimensional simplex, the simplicial chiral models are generalized through replacing the term Tr(AA^{\d}) in the Lagrangian of these models by an arbitrary class function of AA^{\d}; V(AA^{\d}). This is the same method used in defining the generalized two-dimensional Yang-Mills theories (gYM_2) from ordinary YM_2. We call these models, the ``generalized simplicial chiral models''. Using the results of the one-link integral over a U(N) matrix, the large-N saddle-point equations for eigenvalue density function \ro (z) in the weak (\b >\b_c) and strong (\b <\b_c) regions are computed. In d=2, where the model is in some sense related to the gYM_2 theory, the saddle-point equations are solved for \ro (z) in the two regions, and the explicit value of critical point \b_c is calculated for $V(B)$=Tr$B^n$ (B=AA^{\d}). For $V(B$)=Tr$B^2$,Tr$B^3$, and Tr$B^4$, the critical behaviour of the model at d=2 is studied, and by calculating the internal energy, it is shown that these models have a third order phase transition.Comment: 14 pages, LaTex, some minor English corrections, will be published in Nuc. Phys.