A large N phase transition in the continuum two dimensional SU(N) X SU(N) principal chiral model

Using matrix model techniques we investigate the large N limit of generalized 2D Yang-Mills theory. The model has a very rich phase structure. It exhibits multi-critical behavior and reveals a third order phase transitions at all genera besides {\it torus}. This is to be contrasted with ordinary 2D Yang-Mills which, at large N, exhibits phase transition only for spherical topology.

We investigate the principal chiral model between two and four dimensions by means of a non perturbative Wilson-like renormalization group equation. We are thus able to follow the evolution of the effective coupling constants within this whole range of dimensions without having recourse to any kind of small parameter expansion. This allows us to identify its three dimensional critical physics and to solve the long-standing discrepancy between the different perturbative approa...

We extend our previous analysis to arbitrary two dimensional SU(N) principal chiral model in a link formulation. A general expression for the second order coefficient of fixed distance correlation function is given in terms of Green functions. This coefficient is calculated for distance 1 and is proven to be path independent. We also study the weak coupling expansion of the free energy of one dimensional SU(N) model and explain why it is non-uniform in the volume. Further, we...

We study the multiplicity of irreducible representations in the decomposition of $n$ fundamentals of $SU(N)$ weighted by a power of their dimension in the large $n$ and large $N$ double scaling limit. A nontrivial scaling is obtained by keeping $n/N^2$ fixed, which plays the role of an order parameter. We find that the system generically undergoes a fourth order phase transition in this parameter, from a dense phase to a dilute phase. The transition is enhanced to third order...

The SU($N$) principal chiral model is asymptotically free and integrable in $1+1$ dimensions. In the large-$N$ limit, there is no scattering, but correlation functions are {\em not} those of a free field theory. We briefly review the derivation of form factors for local operators. Two-point functions for such operators are known exactly. The two-point function of scaling-field operators has the short-distance behavior expected from the renormalization group. We briefly discus...

We study a $U(N)\times U(N)$ symmetric scalar field model in four and three dimensions. First, using our data in four dimensions in the weak coupling region, we demonstrate explicitly that the observed first order phase transition is induced by quantum fluctuations. Next, based on the renormalization group and our new simulation results in three dimensions we argue that even if the $U_A(1)$ symmetry is restored below the critical temperature the QCD finite temperature chiral ...

The lattice model of principal chiral field interacting with the gauge fields, which have no kinetic term, is considered. This model can be regarded as a strong coupling limit of lattice gauge theory at finite temperature. The complete set of equations for collective field variables is derived in the large N limit and the phase structure of the model is studied.

We investigate the chiral phase transition in SU(N) gauge theories as the number of quark flavors, $N_f$, is varied. We argue that the transition takes place at a large enough value of $N_f$ so that it is governed by the infrared fixed point of the $\beta$ function. We study the nature of the phase transition analytically and numerically, and discuss the spectrum of the theory as the critical value of $N_f$ is approached in both the symmetric and broken phases. Since the tran...

The standard U(N) and SU(N) integrals are calculated in the large N limit. Our main finding is that for an important class of integrals this limit is different for two groups. We describe the critical behaviour of SU(N) models and discuss implications of our results for the large N behaviour of SU(N) lattice gauge theories at finite temperatures and non-zero baryon chemical potential. The key ingredients of our approach are 1) expansion of the integrals into a sum over irredu...

The main focus of this talk is the physics of large N QCD on a continuum torus. A cascade of phase transitions associated with the breaking of U(1) symmetries will be discussed. The continuum Wilson loop as a function of its area will be discussed along with its universality properties and the associated double scaling limit. Some recent progress in twisted Eguchi-Kawai is presented. Gauge field topology and $\theta$ vacuua are also discussed in the context of large N gauge t...