Understanding the cooperative behaviour behind glass transition and more generally glassy dynamics is still a widely open issue. A possible idea, supported by recent evidence for the existence of dynamical heterogeneities, is that the slowing down of dynamics could be related to the motion of defects which becomes increasingly cooperative towards the transition.

We present some analytical results on kinetically constrained lattice models which exhibit glassy dynamics in the high density regime. Despite the simplicity of the local dynamical rules, interesting defect properties emerge which are responsible for the slowing down and heterogeneous character of dynamics. Focusing on Kob-Andersen model as an example, we show that relaxation at high density is due to the cooperative motion of large rare regions where vacancies are configured in special ways. This allows us to prove that no dynamical transition occurs, i.e. the system is ergodic and the self diffusion coefficient is strictly positive at any finite density. Furthermore, from the properties of such defects we predict the density dependence of the diffusion coefficient, which we have successfully checked by numerics. Finally, we discuss the relation among the properties of mobile defects and the form of the dynamical susceptibility. This could provide a way to test the defect scenario for real systems. To obtain a first principle derivation of the conformal field theory describing the edge excitations in a quantum Hall system has been a long standing problem. After reviewing the subject and the main challenges there, we present a microscopic derivation of the field theory of edge excitations (the so-called chiral Luttinger liquid theory) for the Laughlin states. Starting from the wave function describing an arbitrary incompressibly deformed Laughlin state, and using the description of the boundary of the quantum Hall droplet in terms of harmonic moments, we quantize these deformations by defining the explicit action of the creation (annihilation) operators of edge excitations on the many-electron wave-functions. In this way we obtain the low-energy projections of local operators, and derive the quantum field theory of edge excitations directly from quantum mechanics of electrons. We also comment that in the thermodynamic limit the incompressibly deformed Laughlin state is described by the dispersionless Toda hierarchy. Similar techniques have been recently used in the description of the Laplacian growth (Hele-Shaw) problem. We will discuss the predictions of the theory of parton saturation/Color Glass Condensate for particle production in p(d)A collisions. We concentrate on the nuclear modification factor R^pA for gluon production. We show that at moderately high energy/rapidity the nuclear modification factor R^pA exhibits Cronin enhancement. As the energy/rapidity increases, R^pA decreases. At sufficiently high energy/rapidity R^pA becomes less than 1 for all values of p_T indicating the onset of suppression of gluon production due to quantum small-x evolution effects. Our predictions are supported by the recently reported BRAHMS collaboration data on particle production at forward rapidity in dAu collisions at RHIC. .

LPS, ENS