Spontaneous Breaking of Flavor Symmetry and Parity in the Nambu-Jona-Lasinio Model with Wilson Fermions

We study the lattice \njl~model with two flavors of Wilson fermions in the large $N$ limit, where $N$ is the number of `colors'. For large values of the four-fermion coupling we find a phase in which both, flavor symmetry and parity, are spontaneously broken. In accordance with general expectations there are three massless pions on the phase boundary, but only two of them remain massless inside the broken phase. This is analogous to earlier results obtained in lattice QCD, indicating that this behavior is a very general feature of the Wilson term.Comment: 7 pages, 4 figures, LATEX, tared and uuencode

Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere

In the previous papers, we studied the 't Hooft-Polyakov (TP) monopole configurations in the U(2) gauge theory on the fuzzy 2-sphere,and showed that they have nonzero topological charge in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provide a meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that the configuration space can be classified into the topological sectors. We further calculate the spectrum of the GW Dirac operator in the TP monopole backgrounds, and consider the index theorem in these cases.Comment: Latex2e, 37 pages, 3 figure

Passing through the `chiral limit' in quenched QCD with Wilson fermions

We investigate the limit of vanishing quark mass in quenched lattice QCD with unimproved Wilson fermions at $\beta=6.0$. Exploiting the correlations of propagators at different time slices we extract pion masses extremely close to the `chiral limit', despite the presence of `exceptional configurations'. With this at hand, the existence of quenched chiral logarithms can be demonstrated, provided, finite size effects are small. With reference to the phase diagram proposed by Aoki also the range $\kappa > \kappa_c$ is investigated. The width of a potential parity-flavor violating phase can, if at all, hardly be resolved.Comment: LATTICE98(spectrum

Finite-temperature chiral transitions in QCD with the Wilson quark action

We investigate the finite-temperature phase structure and the scaling of the chiral condensate in lattice QCD with two degenerate light quarks, using a renormalization group improved gauge action and the Wilson quark action. We obtain a phase diagram which is consistent with that from the parity-flavor breaking scenario. The scaling relation for the chiral condensate assuming the critical exponents and the scaling function of the three dimensional O(4) model is remarkably satisfied for a wide range of parameters. This indicates that the chiral transition in two flavor QCD is of second order in the continuum limit.Comment: LaTeX, 3 pages, 4 EPS figures, Talk presented at LATTICE97 (finite temperature

Fate of the Critical Line and Chiral Transition in Finite-Temperature Lattice QCD with the Wilson Quark Action

Finite-temperature phase structure of lattice QCD with the Wilson quark action is analyzed. We show that the critical line at finite temperatures, defined to be the line of vanishing pion screening mass, turns back toward strong coupling, forming a cusp on the $(\beta, K)$ plane, and that the line of thermal transition runs past the tip of the cusp without touching the critical line. Previous results are discussed in the light of our findings.Comment: contribution to Lattice 95 (poster session), 4 pages, 4 postscript figure

Electronic structure of an electron on the gyroid surface, a helical labyrinth

Previously reported formulation for electrons on curved periodic surfaces is used to analyze the band structure of an electron bound on the gyroid surface (the only triply-periodic minimal surface that has screw axes). We find that an effect of the helical structure appears as the bands multiply sticking together on the Brillouin zone boundaries. We elaborate how the band sticking is lifted when the helical and inversion symmetries of the structure are degraded. We find from this that the symmetries give rise to prominent peaks in the density of states.Comment: RevTeX, 4 pages, 6 figure

Chiral perturbation theory with Wilson-type fermions including a2a^2 effects: Nf=2N_f=2 degenerate case

We have derived the quark mass dependence of $m_{\pi}^2$, $m_{\rm AWI}$ and $f_{\pi}$, using the chiral perturbation theory which includes the $a^2$ effect associated with the explicit chiral symmetry breaking of the Wilson-type fermions, in the case of the $N_f=2$ degenerate quarks. Distinct features of the results are (1) the additive renormalization for the mass parameter $m_q$ in the Lagrangian, (2) $O(a)$ corrections to the chiral log ($m_q\log m_q$) term, (3) the existence of more singular term, $\log m_q$, generated by $a^2$ contributions, and (4) the existence of both $m_q\log m_q$ and $\log m_q$ terms in the quark mass from the axial Ward-Takahashi identity, $m_{\rm AWI}$. By fitting the mass dependence of $m_\pi^2$ and $m_{\rm AWI}$, obtained by the CP-PACS collaboration for $N_f=2$ full QCD simulations, we have found that the data are consistently described by the derived formulae. Resumming the most singular terms $\log m_q$, we have also derived the modified formulae, which show a better control over the next-to-leading order correction.Comment: 21 pages, 4 figures (10 eps files), Revtex4, some discussions and references added, the final version to appear in PR

The end point of the first-order phase transition of the SU(2) gauge-Higgs model on a four-dimensional isotropic lattice

We report results of a study of the end point of the electroweak phase transition of the SU(2) gauge-Higgs model defined on a four-dimensional isotropic lattice with N_t=2. Finite-size scaling study of Lee-Yang zeros yields lambda_c=0.00116(16) for the end point. Combined with a zero-temperature measurement of Higgs and W boson masses, this leads to M_{H,c}=68.2+-6.6 GeV for the critical Higgs boson mass. An independent analysis of Binder cumulant gives a consistent value lambda_c=0.00102(3) for the end point.Comment: LATTICE98(electroweak), 3 pages of LaTeX, 4 figure

Finite-Temperature Phase Structure of Lattice QCD with the Wilson Quark Action for Two and Four Flavors

We present further analyses of the finite-temperature phase structure of lattice QCD with the Wilson quark action based on spontaneous breakdown of parity-flavor symmetry. Results are reported on (i) an explicit demonstration of spontaneous breakdown of parity-flavor symmetry beyond the critical line, (ii) phase structure and order of chiral transition for the case of $N_f=4$ flavors, and (iii) approach toward the continuum limit.Comment: Poster presented at LATTICE96(finite temperature); 4 pages, Latex, uses espcrc2 and epsf, seven ps figures include