A study of center vortices in SU(2) and SU(3) gauge theories

We show how center vortices and Abelian monopoles both appear as local gauge ambiguities in the Laplacian Center gauge. Numerical results, for SU(2) and SU(3), support the view that the string tension obtained in the center-projected theory matches the full string tension when the continuum limit is taken.Comment: 9 pages, 4 figures; talk presented at the International Workshop on Non-Perturbative Methods and Lattice QCD, Guangzhou, May 200

The phase diagram of N_f=3 QCD for small baryon densities

We demonstrate how to locate the critical endpoint of the QCD phase transition by means of simulations at imaginary \mu. For the three flavor theory, we present numerical results for the pseudo-critical line as a function of chemical potential and bare quark mass, as well as the bare quark mass dependence of the endpoint.Comment: 3 pages, 5 eps-figs, Lattice2003(nonzero

Laplacian Center Vortices

I present a unified picture of center vortices and Abelian monopoles. Both appear as local gauge ambiguities in the Laplacian Center Gauge. This gauge is constructed for a general SU(N) theory. Numerical evidence is presented, for SU(2) and SU(3), that the projected $Z_N$ theory confines with a string tension similar to the non-Abelian one.Comment: 9 pages, 5 figures; talk presented at "Confinement 2000", Osaka, March 200

Adjoint string breaking in 4d SU(2) Yang-Mills theory

We compute the static potential of adjoint sources in SU(2) Yang-Mills theory in four dimensions by numerical Monte Carlo simulations. Following a recent calculation in 2+1 dimensions, we employ a variational approach involving string and gluelump operators and obtain clear evidence for string breaking and the saturation of the potential at large distances. For the string breaking scale we find $r_b \approx 1.25{\rm fm}, 2.3 r_0$, or in units of the lightest glueball, $r_b m_{0++} \approx 9.7$. We furthermore resolve the first excitation of the flux-tube and observe its breaking as well. The result for $r_b$ is in remarkable quantitative agreement with the three-dimensional one.Comment: 15 pages, 3 figures; increased statistics; gauge-fixing clarified; typos correcte

The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density

We present results for the phase diagram of three flavor QCD for \mu_B ~ 500 MeV. Our simulations are performed with imaginary chemical potential \mu_I for which the fermion determinant is positive. Physical observables are then fitted by truncated Taylor series and continued to real chemical potential. We map out the location of the critical line T_c(\mu_B) with an accuracy up to terms of order (\mu_B/T)^6. We also give first results on a determination of the critical endpoint of the transition and its quark mass dependence. Our results for the endpoint differ significantly from those obtained by other methods, and we discuss possible reasons for this.Comment: 20 pages, 10 figures. Eqn (20) corrected, increased statistics, more accurate results. Version to appear in Nucl.Phys.

Truncation Effects in Monte Carlo Renormalization Group Improved Lattice Actions

We study truncation effects in the SU(3) gauge actions obtained by the Monte Carlo renormalization group method. By measuring the heavy quark potential we find that the truncation effects in the actions coarsen the lattice by 40-50 % from the original blocked lattice. On the other hand, we find that rotational symmetry of the heavy quark potentials is well recovered on such coarse lattices, which may indicate that rotational symmetry breaking terms are easily cancelled out by adding a short distance operator. We also discuss the possibility of reducing truncation effects.Comment: 18 pages including 6 figure

QCD at Zero Baryon Density and the Polyakov Loop Paradox

We compare the grand canonical partition function at fixed chemical potential mu with the canonical partition function at fixed baryon number B, formally and by numerical simulations at mu=0 and B=0 with four flavours of staggered quarks. We verify that the free energy densities are equal in the thermodynamic limit, and show that they can be well described by the hadron resonance gas at T T_c. Small differences between the two ensembles, for thermodynamic observables characterising the deconfinement phase transition, vanish with increasing lattice size. These differences are solely caused by contributions of non-zero baryon density sectors, which are exponentially suppressed with increasing volume. The Polyakov loop shows a different behaviour: for all temperatures and volumes, its expectation value is exactly zero in the canonical formulation, whereas it is always non-zero in the commonly used grand-canonical formulation. We clarify this paradoxical difference, and show that the non-vanishing Polyakov loop expectation value is due to contributions of non-zero triality states, which are not physical, because they give zero contribution to the partition function.Comment: 21 pages, 7 figure

Vortex free energies in SO(3) and SU(2) lattice gauge theory

Lattice gauge theories with gauge groups SO(3) and SU(2) are compared. The free energy of electric twist, an order parameter for the confinement-deconfinement transition which does not rely on centre-symmetry breaking, is measured in both theories. The results are used to calibrate the scale in SO(3).Comment: 3 pages, 2 figures, talk presented at Lattice2002(topology