The deconfining phase transition in SU(N) gauge theories

We report on our ongoing investigation of the deconfining phase transition in SU(4) and SU(6) gauge theories. We calculate the critical couplings while taking care to avoid the influence of a nearby bulk phase transition. We determine the latent heat of the phase transition and investigate the order and the strength of the transition at large N. We also report on our determination of the critical temperature expressed in units of the string tension in the large N limit.Comment: Lattice 2002 (nonzerot), 3 pages, 2 figure

Features of SU(N) Gauge Theories

We review recent lattice results for the large $N$ limit of SU(N) gauge theories. In particular, we focus on glueball masses, topology and its relation to chiral symmetry breaking (relevant for phenomenology), on the tension of strings connecting sources in higher representations of the gauge group (relevant for models of confinement and as a comparative ground for theories beyond the Standard Model) and on the finite temperature deconfinement phase transition (relevant for RHIC-like experiments). In the final part we present open challenges for the future.Comment: 6 pages, 3 figures; summary of the talk given by B. Lucini and the poster presented by U. Wenger at the conference "Confinement 2003

HMC algorithm with multiple time scale integration and mass preconditioning

We describe a new HMC algorithm variant we have recently introduced and extend the published results by preliminary results of a simulation with a pseudo scalar mass value of about 300 MeV. This new run confirms our expectation that simulations with such pseudo scalar mass values become feasible and affordable with our HMC variant. In addition we discuss simulations from hot and cold starts at a pseudo scalar mass value of about 300 MeV, which we performed in order to test for possible meta-stabilities.Comment: 6 pages, Talk presented at Lattice 2005 (machines and algorithms

A comparative study of overlap and staggered fermions in QCD

We perform a comparative study of the infrared properties of overlap and staggered fermions in QCD. We observe that the infrared spectrum of the APE/HYP improved staggered Dirac operator develops a four-fold near-degeneracy and is in quantitative agreement with the infrared spectrum of the overlap operator. The near-degeneracy allows us to identify the zero modes of the staggered operator and we find that the number of zero modes is in line with the topological index of the overlap operator.Comment: Talk presented at Lattice2004(chiral), Fermilab, June 21-26, 2004, 3 pages, 2 figure

Progress using generalized lattice Dirac operators to parametrize the Fixed-Point QCD action

We report on an ongoing project to parametrize the Fixed-Point Dirac operator for massless quarks, using a very general construction which has arbitrarily many fermion offsets and gauge paths, the complete Clifford algebra and satisfies all required symmetries. Optimizing a specific construction with hypercubic fermion offsets, we present some preliminary results.Comment: Lattice 2000 (Improvement), 9 pages, based on a talk by K.H. and a poster by T.J. References adde

The construction of generalized Dirac operators on the lattice

We discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic rotations and reflections) on the lattice. We give an extensive set of examples and offer help to add further structures.Comment: 19 pages, latex, maple code attache

Baryonic matter in the lattice Gross-Neveu model

We investigate the Gross-Neveu model on the lattice at finite temperature and chemical potential in the limit of an infinite number of fermion flavours. We check the universality of the continuum limit of staggered and overlap fermions at finite temperature and chemical potential. We show that at finite density a recently discovered phase of cold baryonic matter emerges as a baryon crystal from a spatially inhomogeneous fermion condensate. However, we also demonstrate that on the lattice, this new phase disappears at large coupling or in small volumes. Furthermore, we investigate unusual finite size effects that appear at finite chemical potential. Finally, we speculate on the implications of our findings for QCD

Chiral symmetry breaking and topology for all N

We investigate spontaneous chiral symmetry breaking in SU(N) gauge theories at large N using overlap fermions. The exact zero modes and the low-lying modes of the Dirac operator provide the tools to gain insight into the interplay between chiral symmetry breaking and topology. We find that topology indeed drives chiral symmetry breaking at N=3 as well as at large N. By comparing the results on various volumes and at different lattice spacings we are able to show that our conclusions are not affected by finite volume effects and also hold in the continuum limit. We then address the question whether the topology can be usefully described in terms of instantons.Comment: Talk at Lattice 2003 (chiral); 3 pages, 2 figures, espcrc2.st

The overlap operator as a continued fraction

We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method where nested conjugate gradient procedures are avoided. We show that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions. This is of significant importance when dynamical overlap fermions are simulated.Comment: 3 pages, 1 figure, talk presented by U. Wenger at Lattice2001(chiral

On the phase diagram of QCD at finite isospin density

Using a canonical formalism, we determine the equation of state and the phase diagram of eight-flavour QCD, as a function of temperature and isospin density. Two mechanisms are at work: Bose condensation of pions at high density, and deconfinement at high temperature. We study their interplay and find that on our small and coarse lattice the first order deconfinement transition appears to end at a critical point at finite density. We investigate the strength of the overlap and of the sign problems and discuss implications for the baryonic density case.Comment: 7 pages, 4 figures, Contribution to Lattice 2007, Regensburg, Germany, 30 July - 4 August 200