Lattice QCD without topology barriers

As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.Comment: Plain TeX source, 26 pages, 4 figures include

The gradient flow running coupling with twisted boundary conditions

We study the gradient flow for Yang-Mills theories with twisted boundary conditions. The perturbative behavior of the energy density $\langle E(t)\rangle$ is used to define a running coupling at a scale given by the linear size of the finite volume box. We compute the non-perturbative running of the pure gauge $SU(2)$ coupling constant and conclude that the technique is well suited for further applications due to the relatively mild cutoff effects of the step scaling function and the high numerical precision that can be achieved in lattice simulations. We also comment on the inclusion of matter fields.Comment: 27 pages. LaTe

Testing a Topology Conserving Gauge Action in QCD

We study lattice QCD with a gauge action, which suppresses small plaquette values. Thus the MC history is confined to a single topological sector over a significant time, while other observables are decorrelated. This enables the cumulation of statistics with a specific topological charge, which is needed for simulations of QCD in the $\epsilon$-regime. The same action may also be useful for simulations with dynamical quarks. The update is performed with a local HMC algorithm.Comment: 3 pages, 3 figures, poster presented by S. Shcheredin at Lattice2004(theory

The Landau Pole at Finite Temperature

We study the Landau pole in the lambda phi^4 field theory at non-zero and large temperatures. We show that the position of the thermal Landau pole Lambda_L(T) is shifted to higher energies with respect to the zero temperature Landau pole Lambda_L(0). We find for high temperatures T > Lambda_L(0), Lambda_L(T) simeq pi^2 T / log (T / Lambda_L(0)). Therefore, the range of applicability in energy of the lambda phi^4 field theory increases with the temperature.Comment: LaTex, 6 pages, 2 .ps figures. Improved version. To appear in Phys. Rev. D, Rapid Communication

Short distance behaviour of the effective string

We study the Polyakov loop correlator in the (2+1) dimensional Z_2 gauge model. An algorithm that we have presented recently, allows us to reach high precision results for a large range of distances and temperatures, giving us the opportunity to test predictions of the effective Nambu-Goto string model. Here we focus on the regime of low temperatures and small distances. In contrast to the high temperature, large distance regime, we find that our numerical results are not well described by the two loop-prediction of the Nambu-Goto model. In addition we compare our data with those for the SU(2) and SU(3) gauge models in (2+1) dimensions obtained by other authors. We generalize the result of L\"uscher and Weisz for a boundary term in the interquark potential to the finite temperature case.Comment: 38 pages, 7 figures, version accepted for publication in JHE

SU(3) lattice gauge theory with a mixed fundamental and adjoint plaquette action: Lattice artefacts

We study the four-dimensional SU(3) gauge model with a fundamental and an adjoint plaquette term in the action. We investigate whether corrections to scaling can be reduced by using a negative value of the adjoint coupling. To this end, we have studied the finite temperature phase transition, the static potential and the mass of the 0^{++} glueball. In order to compute these quantities we have implemented variance reduced estimators that have been proposed recently. Corrections to scaling are analysed in dimensionless combinations such as T_c/\sqrt{\sigma} and m_{0^{++}}/T_c. We find that indeed the lattice artefacts in e.g. m_{0^{++}}/T_c can be reduced considerably compared with the pure Wilson (fundamental) gauge action at the same lattice spacing.Comment: 36 pages, 12 figure

The running coupling of 8 flavors and 3 colors

We compute the renormalized running coupling of SU(3) gauge theory coupled to N_f = 8 flavors of massless fundamental Dirac fermions. The recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings allowing for a controlled continuum extrapolation. The results for the discrete beta-function show that it is monotonic without any sign of a fixed point in the range of couplings we cover. As a cross check the continuum results are compared with the well-known perturbative continuum beta-function for small values of the renormalized coupling and perfect agreement is found.Comment: 15 pages, 17 figures, published versio

Recent Developments in Lattice QCD

I review the current status of lattice QCD results. I concentrate on new analytical developments and on numerical results relevant to phenomenology.Comment: 35 pages, 4 figures (Figures are excerpted from others' work and are not included) Uses harvmac.te

Nuclear Physics from lattice QCD at strong coupling

We study numerically the strong coupling limit of lattice QCD with one flavor of massless staggered quarks. We determine the complete phase diagram as a function of temperature and chemical potential, including a tricritical point. We clarify the nature of the low temperature dense phase, which is strongly bound nuclear matter. This strong binding is explained by the nuclear potential, which we measure. Finally, we determine, from this first-principle limiting case of QCD, the masses of atomic nuclei up to A=12 "carbon".Comment: 4 pages, 5 figures; v2: references added, minor changes, published versio

Speeding up finite step-size updating of full QCD on the lattice

We propose various improvements of finite step-size updating for full QCD on the lattice that might turn finite step-size updating into a viable alternative to the hybrid Monte Carlo algorithm. These improvements are noise reduction of the noisy estimator of the fermion determinant, unbiased inclusion of the hopping parameter expansion and a multi-level Metropolis scheme. First numerical tests are performed for the 2 dimensional Schwinger model with two flavours of Wilson fermions and for QCD two flavours of Wilson fermions and Schr"odinger functional boundary conditions.Comment: 22 pages, 1 figur