Study of θ\theta dependence in Yang-Mills theories on the lattice

We discuss the use of field theoretical techniques in the lattice determination of the free energy dependence on the $\theta$ angle in SU(N) Yang-Mills theories.Comment: 5 pages. Talk at the International Workshop on QCD: QCD@Work 2003 - Conversano (Italy) 14-18 June 2003 (eConf C030614

Field theoretical approach to the study of theta dependence in Yang-Mills theories on the lattice

We discuss the extension of the field theoretical approach, already used in the lattice determination of the topological susceptibility, to the computation of further terms in the expansion of the ground state energy $F(\theta)$ around $\theta = 0$ in SU(N) Yang-Mills theories. In particular we determine the fourth order term in the expansion for SU(3) pure gauge theory and compare our results with previous cooling determinations. In the last part of the paper we make some considerations about the nature of the ultraviolet fluctuations responsible for the renormalization of the lattice topological charge correlation functions; in particular we propose and test an ansatz which leads to improved estimates of the fourth and higher order terms in the expansion of F(\theta).Comment: 20 page

High-Temperature QCD: theory overview

We review the recent progress achieved in the theoretical investigation of Quantum Chromodynamics in the high temperature regime, with a focus on results achieved by lattice QCD simulations. The discussion covers the structure of the phase diagram and the properties of the strongly interacting medium at finite T and small baryon chemical potential.Comment: 7 pages, 2 figures, Proceedings of the Quark Matter 2018 conference, Venice, Ital

Predictions vs preliminary sample estimates

In general, rational economic agents are not in the position to wait for the statistical agencies disseminate the final results of the relevant surveys before making a decision, and have to make use of some model based predictions, even when agents are not assumedly forward looking. Thus, from the viewpoint of agents, predictions and preliminary results from surveys often compete against each other. Agents are aware to incur in a loss basing their decisions on predictions instead of sound statistical data, but the loss could be smaller than the one related to waiting for the dissemination of final data. Comparing the loss attached to predictions, on the one hand, and to possible preliminary estimate from incomplete samples, on the other, provides a broad guidance in deciding if and when statistical agencies should release preliminary and final estimates of the key variables. The main result of the analysis is that, in general, preliminary sample estimates are useful for the users only if they come from unexpectedly large sub-samples, even when the predictability of relevant variables is scarce. Nevertheless, the cost of delaying decisions for many economic agents may support the dissemination of early estimates of the main economic aggregates even if their accuracy is not fully satisfactory from a strict statistical viewpoint.Accuracy; Data Dissemination; Forecast; Preliminary Estimates; Timeliness

Topology on the Lattice

We review the method developed in Pisa to determine the topological susceptibility in lattice QCD and present a collection of new and old results obtained by the method.Comment: 10 pages, 7 figures. Contribution to "Sense of Beauty in Physics - a volume in honour of Adriano Di Giacomo" (Pisa University Press, Pisa, 2006), on the occasion of his 70th birthda

Phase structure of compactified SU(N)SU(N) gauge theories in magnetic backgrounds

We discuss the properties of non-abelian gauge theories formulated on manifolds with compactified dimensions and in the presence of fermionic fields coupled to magnetic backgrounds. We show that different phases may emerge, corresponding to different realizations of center symmetry and translational invariance, depending on the compactification radius and on the magnitude of the magnetic field. Our discussion focuses on the case of an $SU(3)$ gauge theory in 4 dimensions with fermions fields in the fundamental representation, for which we provide some exploratory numerical lattice results.Comment: 5 pages, 7 figure

Spectrum of the Laplace-Beltrami Operator and the Phase Structure of Causal Dynamical Triangulation

We propose a new method to characterize the different phases observed in the non-perturbative numerical approach to quantum gravity known as Causal Dynamical Triangulation. The method is based on the analysis of the eigenvalues and the eigenvectors of the Laplace-Beltrami operator computed on the triangulations: it generalizes previous works based on the analysis of diffusive processes and proves capable of providing more detailed information on the geometric properties of the triangulations. In particular, we apply the method to the analysis of spatial slices, showing that the different phases can be characterized by a new order parameter related to the presence or absence of a gap in the spectrum of the Laplace-Beltrami operator, and deriving an effective dimensionality of the slices at the different scales. We also propose quantities derived from the spectrum that could be used to monitor the running to the continuum limit around a suitable critical point in the phase diagram, if any is found.Comment: 21 pages, 26 figures, 2 table

QCD Thermodynamics: Lattice Results confront Models

We show that lattice results on four flavor QCD at nonzero temperature and baryon density compare well with the hadron resonance gas model up to T approx. 0.95 Tc, and approach a free field behaviour with a reduced effective number of flavor for T \ge 1.5 Tc. Chiral symmetry and confinement are interrelated, and we note analogies between the critical line of QCD and that of simple models with the same global symmetries.Comment: 5 pages, 4 figures; talk given at the conference Strong and Electroweak Matter 2004, Helsinki, Finland, 16-19 June 200

QCD Critical Region and Quark Gluon Plasma from an Imaginary mu_B

We discuss the imaginary chemical potential approach to the study of QCD at nonzero temperature and density, present results for the four flavor model in the different phases and show that this method is ideally suited for a comparison between lattice data and phenomenological models.Comment: 3 pages, Lattice2003(nonzero); references adde