Adriano Di Giacomo

Topological charge, renormalization and cooling on the lattice☆

Abstract We show that a definition of the topological susceptibility χ on the lattice in terms of local fields, with the proper additive and multiplicative renormalizations, is well defined, self-consistent and compatible with results we obtain by the cooling method. Moreover, we can follow the behaviour of the multiplicative renormalization during cooling, and check its dependence on the coupling constant.

Two flavor QCD and confinement

We argue that the order of the chiral transition for N_f=2 is a sensitive probe of the QCD vacuum, in particular of the mechanism of color confinement. A strategy is developed to investigate the order of the transition by use of finite size scaling analysis. An in-depth numerical investigation is performed with staggered fermions on lattices with N_t=4 and N_s=12,16,20,24,32 and quark masses am_q ranging from 0.01335 to 0.307036. The specific heat and a number of susceptibilities are measured and compared with the expectations of an O(4) second order and of a first order phase transition. A second order transition in the O(4) and O(2) universality classes are excluded. Substantial evidence emerges for a first order transition. A detailed comparison with previous works is performed.

Renormalization and topological susceptibility on the lattice

Abstract We study the renormalization of the topological susceptibility, χ, when the density of topological charge is defined as a local operator on the lattice. In the 2D O(3) δ model we determine both multiplicative and additive renormalizations by heating configurations with a definite number of instantons. We find results that are consistent with perturbation theory. The method is also applicable to the physically interesting case of 4D non-abelian gauge theories.

Cooling and the string tension in lattice gauge theories

Abstract We explore the possibility of improving the determination of the string tension using the cooling method. We present preliminary results for the gauge group SU(2): We find that statistical errors are drastically reduced and at the same time the string tension is preserved through many cooling steps.

G_2 gauge theory at finite temperature

The gauge group being centreless, G2 gauge theory is a good laboratory for studying the role of the centre of the group for colour confinement in Yang-Mills gauge theories. In this paper, we investigate G2 pure gauge theory at finite temperature on the lattice. By studying the finite size scaling of the plaquette, the Polyakov loop and their susceptibilities, we show that a deconfinement phase transition takes place. The analysis of the pseudocritical exponents give strong evidence of the deconfinement transition being first order. Implications of our findings for scenarios of colour confinement are discussed.

Evidence for flux tubes from cooled QCD configurations

Abstract We analyze field configurations between a static qq in SU(2) lattice gauge theory using a cooling technique, which reduces quantum fluctuations while preserving the string tension and the topological charge. We find clear evidence of chromoelectric flux tube configurations, of transverse size which scales properly and in physical units is of the order of about 0.4 fm.

Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory.

The renormalization functions involved in the determination of the topological susceptibility in the SU(2) lattice gauge theory are extracted by direct measurements, without relying on perturbation theory. The determination exploits the phenomenon of critical slowing down to allow the separation of perturbative and non-perturbative effects. The results are in good agreement with perturbative computations.

Gluon condensation in SU(3) lattice gauge theory

Abstract The gluon condensate of dimension 4 is determined for a gauge SU(3) lattice gauge theory. A critical review of the existing procedures to extract the condensate is presented.

Improved lattice operators: Case of the topological charge density

We analyze the properties of a class of improved lattice topological charge density operators, constructed by a smearinglike procedure. By optimizing the choice of the parameters introduced in their definition we find operators having (i) a better statistical behavior as estimators of the topological charge density on the lattice, i.e., less noisy, (ii) a multiplicative renormalization much closer to one, and (iii) a large suppression of the perturbative tail (and other unphysical mixings) in the corresponding lattice topological susceptibility. {copyright} {ital 1996 The American Physical Society.}

THE TOPOLOGICAL SUSCEPTIBILITY AND LATTICE UNIVERSALITY

Abstract We study the topological susceptibility χ on the lattice, using four different actions from the mixed fundamental adjoint family. To measure χ we employ on the one hand a field theoretic approach, which requires the calculation of lattice-induced renormalization functions, to be applied to the raw Monte Carlo data; on the other hand we use a method of slow cooling. The two methods provide cross-checks on each other and are found to give consistent results. We also measure with the same actions the quadratic gluon condensate G2 and the string tension σ; the latter can be measured with very small statistical flutuations using cooling. The dimensionless ratios χ/G2 and σ2/G2 must be the same for all actions and we thus use them to test universality, independently of any prescriptions for the values of ΛQCD or for the scaling region in each action. We also carry out checks of three such prescriptions for a comparative evaluation.