Chiral symmetry breaking at large N_c

We present numerical evidence for the hypothesis that, in the planar limit, four dimensional Euclidean Yang-Mills theory on a finite symmetrical four-torus breaks chiral symmetry spontaneously when the length of the sides l is larger than a critical value l_c with a bilinear condensate whose value is independent of l. Therefore spontaneous symmetry breaking occurs at finite volume and infinite N_c reduction holds for the chiral condensate.Comment: 43 pages, 16 figures, 1 table, more typos correcte

Chiral Anomaly and Index Theorem on a finite lattice

The condition for a lattice Dirac operator D to reproduce correct chiral anomaly at each site of a finite lattice for smooth background gauge fields is that D possesses exact zero modes satisfying the Atiyah-Singer index theorem. This is also the necessary condition for D to have correct fermion determinant (ratio) which plays the important role of incorporating dynamical fermions in the functional integral.Comment: LATTICE99(chiral fermion), 3 pages, Latex, espcrc2.st

The overlap lattice Dirac operator and dynamical fermions

I show how to avoid a two level nested conjugate gradient procedure in the context of Hybrid Monte Carlo with the overlap fermionic action. The resulting procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but is more flexible and therefore has some potential worth exploring.Comment: Further expanded version. 12 pages, plain Te

Topological Phases in Neuberger-Dirac operator

The response of the Neuberger-Dirac fermion operator D=\Id + V in the topologically nontrivial background gauge field depends on the negative mass parameter $m_0$ in the Wilson-Dirac fermion operator $D_w$ which enters $D$ through the unitary operator $V = D_w (D_w^{\dagger} D_w)^{-1/2}$. We classify the topological phases of $D$ by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise

Noncompact chiral U(1) gauge theories on the lattice

A new, adiabatic phase choice is adopted for the overlap in the case of an infinite volume, noncompact abelian chiral gauge theory. This gauge choice obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in addition, produces a Wess-Zumino functional that is linear in the gauge variables on the lattice. As a result, there are no gauge violations on the trivial orbit in all theories, consistent and covariant anomalies are simply related and Berry's curvature now appears as a Schwinger term. The adiabatic phase choice can be further improved to produce a perfect phase choice, with a lattice Wess-Zumino functional that is just as simple as the one in continuum. When perturbative anomalies cancel, gauge invariance in the fermionic sector is fully restored. The lattice effective action describing an anomalous abelian gauge theory has an explicit form, close to one analyzed in the past in a perturbative continuum framework.Comment: 35 pages, one figure, plain TeX; minor typos corrected; to appear in PR

Proposal for the numerical solution of planar QCD

Using quenched reduction, we propose a method for the numerical calculation of meson correlation functions in the planar limit of QCD. General features of the approach are outlined, and an example is given in the context of two-dimensional QCD.Comment: 31 pages, 10 figures, uses axodraw.sty, To appear in Physical Review

Improving meson two-point functions by low-mode averaging

Some meson correlation functions have a large contribution from the low lying eigenmodes of the Dirac operator. The contribution of these eigenmodes can be averaged over all positions of the source. This can improve the signal in these channels significantly. We test the method for meson two-point functions.Comment: Talk given at Lattice2004(spectrum), Fermilab, June 21-26, 200

A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator

We compute fermionic observables relevant to the study of chiral symmetry in quenched QCD using the Overlap-Dirac operator for a wide range of the fermion mass. We use analytical results to disentangle the contribution from exact zero modes and simplify our numerical computations. Details concerning the numerical implementation of the Overlap-Dirac operator are presented.Comment: 24 pages revtex with 5 postscript figures included by eps

Bounds on the Wilson Dirac Operator

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator. The bounds also apply to the Wilson Dirac operator in odd dimensions and are therefore relevant to domain wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement

Energy minimization using Sobolev gradients: application to phase separation and ordering

A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to functionals describing coarse-grained Ginzburg-Landau models commonly used in pattern formation and ordering processes.Comment: To appear J. Computational Physic