A non perturbative approach of the principal chiral model between two and four dimensions

We analyze the dynamical chiral symmetry breaking in gauge theories solely by the non-perturbative renormalization group, without recourse to the Schwinger-Dyson method. First, we briefly review the basic notions and formulation, and clarify its great feature that it gives a systematic approximation scheme without any divergent series nor serious gauge dependence, compared to other perturbative and non-perturbative methods. Then we apply this new method to QED and QCD to find...

An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.

It is established by numerical means that the continuum large N principal chiral model in two dimensions has a phase transition in a smoothed two point function at a critical distance of the order of the correlation length.

The behaviour of a d-dimensional vectorial N=3 model at a m-axial Lifshitz critical point is investigated by means of a nonperturbative renormalization group approach that is free of the huge technical difficulties that plague the perturbative approaches and limit their computations to the lowest orders. In particular being systematically improvable, our approach allows us to control the convergence of successive approximations and thus to get reliable physical quantities in ...

Contents: 1. Introduction, 2. Chiral gauge theories & the gauge anomaly, 3. The regularization problem, 4. Weyl fermions from 4+1 dimensions, 5. The Ginsparg-Wilson relation, 6. Gauge-invariant lattice regularization of anomaly-free theories.

An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.

On the example of the three-dimensional Ising model, we show that nonperturbative renormalization group equations allow one to obtain very accurate critical exponents. Implementing the order $\partial^4$ of the derivative expansion leads to $\nu=0.632$ and to an anomalous dimension $\eta=0.033$ which is significantly improved compared with lower orders calculations.

We consider the model of a massless charged scalar field, in (2+1) dimensions, with a self interaction of the form $lambda (\phi^* \phi)^3$ and interacting with a Chern Simons field. We calculate the renormalization group $\beta$ functions of the coupling constants and the anomalous dimensions $\gamma$ of the basic fields. We show that the interaction with the Chern Simons field implies in a $\beta_{\lambda}$ which suggests that a dynamical symmetry breakdown occurs. We also ...

We study the non relativistic limit of a Model of Fermions interacting through a Chern-Simons Field, from a perspective that resembles the Wilson's Renormalization Group approach, instead of the more usual approach found in most texts of Field Theory. The solution of some difficulties, and a new understanding of non relativistic models is given.

We carry out a high-precision simulation of the two-dimensional $SU(3)$ principal chiral model at correlation lengths $\xi$ up to $\approx\! 4 \times 10^5$, using a multi-grid Monte Carlo (MGMC) algorithm. We extrapolate the finite-volume Monte Carlo data to infinite volume using finite-size-scaling theory, and we discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. For $...