Principal Chiral Field at Large N

A low energy bound in a class of chiral solitonic field theories related the infrared physics of the SU(N) Yang-Mills theory is established.

We investigate fermionic quantum field theories using functional renormalisation. In the limit of many fermion flavours $N$, we demonstrate that theories have exact solutions for their quantum effective actions given by quasi-local interaction functionals of fermion bilinears. The structure implies that local potential approximations are exact, exactly solvable, and that field anomalous dimensions vanish. Theories with non-trivial anomalous dimensions may also arise under con...

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 ...

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.

We examine the precise structure of the loop algebra of `dressing' symmetries of the Principal Chiral Model, and discuss a new infinite set of abelian symmetries of the field equations which preserve a symplectic form on the space of solutions.

The exact renormalization group approach (ERG) is developed for the case of pure fermionic theories by deriving a Grassmann version of the ERG equation and applying it to the study of fixed point solutions and critical exponents of the two-dimensional chiral Gross-Neveu model. An approximation based on the derivative expansion and a further truncation in the number of fields is used. Two solutions are obtained analytically in the limit $N\to \infty $, with N being the number ...

Conformal theories with a global symmetry may be studied in the double scaling regime where the interaction strength is reduced while the global charge increases. Here, we study generic 4d $\mathcal N=2$ $SU(N)$ gauge theories with conformal matter content at large R-charge $Q_{\rm R}\to \infty$ with fixed 't Hooft-like coupling $\kappa = Q_{\rm R}\,g_{\rm YM}^{2}$. Our analysis concerns two distinct classes of natural scaling functions. The first is built in terms of chiral/...

Following recent advances in large N matrix mechanics, I discuss here the free (Cuntz) algebraic formulation of the large N limit of two-dimensional conformal field theories of chiral adjoint fermions and bosons. One of the central results is a new {\it affine free algebra} which describes a large N limit of su(N) affine Lie algebra. Other results include the associated {\it free-algebraic partition functions and characters}, a free-algebraic coset construction, free- algebra...

We study the integrable bi-Yang-Baxter deformation of the $SU(2)$ principal chiral model (PCM) and its finite action uniton solutions. Under an adiabatic compactification on an $S^1$, we obtain a quantum mechanics with an elliptic Lam\'e-like potential. We perform a perturbative calculation of the ground state energy in this quantum mechanics to large orders obtaining an asymptotic series. Using the Borel-Pad\'e technique, we determine the expected locations of branch cuts ...

We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar $U(\phib^2)$ field theory for $N$ large and discuss various non-perturbative physical issue...