Theta dependence of SU(N) gauge theories in the presence of a topological term

We review results concerning the theta dependence of 4D SU(N) gauge theories and QCD, where theta is the coefficient of the CP-violating topological term in the Lagrangian. In particular, we discuss theta dependence in the large-N limit. Most results have been obtained within the lattice formulation of the theory via numerical simulations, which allow to investigate the theta dependence of the ground-state energy and the spectrum around theta=0 by determining the moments of the topological charge distribution, and their correlations with other observables. We discuss the various methods which have been employed to determine the topological susceptibility, and higher-order terms of the theta expansion. We review results at zero and finite temperature. We show that the results support the scenario obtained by general large-N scaling arguments, and in particular the Witten-Veneziano mechanism to explain the U(1)_A problem. We also compare with results obtained by other approaches, especially in the large-N limit, where the issue has been also addressed using, for example, the AdS/CFT correspondence. We discuss issues related to theta dependence in full QCD: the neutron electric dipole moment, the dependence of the topological susceptibility on the quark masses, the U(1)_A symmetry breaking at finite temperature. We also consider the 2D CP(N) model, which is an interesting theoretical laboratory to study issues related to topology. We review analytical results in the large-N limit, and numerical results within its lattice formulation. Finally, we discuss the main features of the two-point correlation function of the topological charge density.

Relaxational dynamics in 3D randomly diluted Ising models

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2).

SU(N) gauge theories in the presence of a topological term

We review recent results on the theta dependence of the ground-state energy and spectrum of four-dimensional SU(N) gauge theories, where theta is the coefficient of the CP-violating topological term F-Fdual in the Lagrangian. In particular, we discuss the results obtained by Monte Carlo simulations of the lattice formulation of QCD, which allow the investigation of theta dependence around theta=0 by determining the moments of the topological charge distribution, and their correlations with other observables. The results for N=3 and larger values of N support the scenario obtained by general large-N scaling arguments.