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

We study the Principal Chiral Ginzburg-Landau-Wilson model around two dimensions within the Local Potential Approximation of an Exact Renormalization Group equation. This model, relevant for the long distance physics of classical frustrated spin systems, exhibits a fixed point of the same universality class that the corresponding Non-Linear Sigma model. This allows to shed light on the long-standing discrepancy between the different perturbative approaches of frustrated spin ...

We present results from numerical simulations of three different 3d four-fermion models that exhibit Z_2, U(1), and SU(2) x SU(2) chiral symmetries, respectively. We performed the simulations by using the hybrid Monte Carlo algorithm. We employed finite size scaling methods on lattices ranging from 8^3 to 40^3 to study the properties of the second order chiral phase transition in each model. The corresponding critical coupling defines an ultraviolet fixed point of the renorma...

We report the explicit solution for the vacuum state of the two-dimensional $SU(N)$ Principal Chiral Model at large-$N$ for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an asymptotically free QFT. The solution matches one-loop perturbative calculation at weak coupling, and in the opposite strong-coupling regime exhibits an emergent spacial dimension from the continuum limit of the $SU(N)$ Dynkin diagram.

We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean $SU(2)$ principal chiral field model with the triad tensor renormalization group (tTRG) and the anisotropic tensor renormalization group (ATRG) methods. Using these methods, we find results that are consistent with previous Monte Carlo estimates and the predicted renormalization group scaling of the magnetization close to criticality. These results bring us one step close...

The critical dynamics of the chiral symmetry breaking induced by gauge interaction is examined in the Wilson renormalization group framework in comparison with the Schwinger-Dyson approach. We derive the beta functions for the four-fermi couplings in the sharp cutoff renormalzation group scheme, from which the critical couplings and the anomalous dimensions of the fermion composite operators near criticality are immediately obtained. It is also shown that the beta functions l...

We consider a two-dimensional scalar field theory with a nilpotent current algebra, which is dual to the Principal Chiral Model. The quantum theory is renormalizable and not asymptotically free: the theory is strongly coupled at short distances (encountering a Landau pole). We suggest it can serve as a toy model for $\lambda\phi^{4}$ theory in four dimensions, just as the principal chiral model is a useful toy model for Yang-Mills theory. We find some classical wave solutions...

Basic elements of the exact renormalization group method and recent results within this approach are reviewed. Topics covered are the derivation of equations for the effective action and relations between them, derivative expansion, solutions of fixed point equations and the calculation of the critical exponents, construction of the c-function and a description of the chiral phase transition.

We formulate the two-dimensional principal chiral model as a quantum spin model, replacing the classical fields by quantum operators acting in a Hilbert space, and introducing an additional, Euclidean time dimension. Using coherent state path integral techniques, we show that in the limit in which a large representation is chosen for the operators, the low energy excitations of the model describe a principal chiral model in three dimensions. By dimensional reduction, the two-...

We study the chiral critical behaviors of QED by using Non-Perturbative Renormalization Group (NPRG). Taking account of the non-ladder contributions, our flow equations are free from the gauge parameter ($\alpha$) dependence. We clarify the chiral phase structure, and calculate the anomalous dimension of $\bar\psi\psi$, which is enhanced compared to the ladder approximation. We find that the cutoff scheme dependence of the physical results is very small.

We initiate a systematic, non-perturbative study of the large-$N$ expansion in the two-dimensional $\text{SU}(N)\times \text{SU}(N)$ Principal Chiral Model (PCM). Starting with the known infinite-$N$ solution for the ground state at fixed chemical potential \cite{Fateev:1994dp,Fateev:1994ai}, we devise an iterative procedure to solve the Bethe ansatz equations order by order in $1/N$. The first few orders, which we explicitly compute, reveal a systematic enhancement pattern a...