SU(3) Lattice Gauge Theory in the Fundamental--Adjoint Plane and Scaling Along the Wilson Axis

We present further evidence for the bulk nature of the phase transition line in the fundamental--adjoint action plane of SU(3) lattice gauge theory. Computing the string tension and some glueball masses along the thermal phase transition line of finite temperature systems with $N_t=4$, which was found to join onto the bulk transition line at its endpoint, we find that the ratio $\sqrt{\sigma} / T_c$ remains approximately constant. However, the mass of the $0^{++}$ glueball decreases as the endpoint of the bulk transition line is approached, while the other glueball masses appear unchanged. This is consistent with the notion that the bulk transition line ends in a critical endpoint, with the continuum limit there being a $\phi^4$ theory with a diverging correlation length only in the $0^{++}$ channel. We comment on the implications for the scaling behavior along the fundamental or Wilson axis.Comment: 10 pages. Plain LaTeX file. 4 postscript figures added in a separate fil

A new method to measure the chiral condensate in lattice QCD using Wilson fermions

Parity and flavor symmetry is not broken in QCD. Using this fact, we propose a new method to measure the chiral condensate in lattice QCD using Wilson fermions with an operator that breaks parity and flavor in addition to the chiral symmetry.Comment: 9 pages, LaTeX, no figure

Wilson chiral perturbation theory, Wilson-Dirac operator eigenvalues and clover improvement

Chiral perturbation theory for eigenvalue distributions, and equivalently random matrix theory, has recently been extended to include lattice effects for Wilson fermions. We test the predictions by comparison to eigenvalue distributions of the Hermitian Wilson-Dirac operator from pure gauge (quenched) ensembles. We show that the lattice effects are diminished when using clover improvement for the Dirac operator. We demonstrate that the leading Wilson low-energy constants associated with Wilson (clover) fermions can be determined using spectral information of the respective Dirac operator at finite volume.Comment: Presented at "Xth Quark Confinement and the Hadron Spectrum," October 2012, Garching, Germany. To appear as PoS (Confinement X) 07

The Schr\"odinger functional running coupling with staggered fermions and its application to many flavor QCD

We discuss the Schr\"odinger functional in lattice QCD with staggered fermions and relate it, in the classical continuum limit, to the Schr\"odinger functional regularized with Wilson fermions. We compute the strong coupling constant defined via the Schr\"odinger functional with staggered fermions at one loop and show that it agrees with the continuum running coupling constant in the Schr\"odinger functional formalism. We compute this running coupling in the ``weak coupling phase'' of many flavor QCD numerically at several values of the bare coupling and for several system sizes from $L/a=4$ to 12. The results indicate that the $\beta$-function for 16 flavors has the opposite sign than for few flavor QCD, in agreement with a recent claim, and with the perturbative prediction.Comment: 3 pages with 2 ps figures; to appear in the proceedings of Lattice '97, Edinburgh, Scotland, July 22--26, 199