A largeNphase transition in the continuum two dimensional SU(N) × SU(N) principal chiral model

Abstract

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.

gauge theories at large

“…Recent examples of analytical results in 2D models of QCD at large N include, e.g., those obtained in the study of form factors in the principal chiral model [1040][1041][1042]-a theory which has also been studied numerically [1043] (see also Ref. [1044]).…”

Eigenvalue density of Wilson loops in 2DSU(N) YM

“…This phase transition has universal properties shared across dimensions and across analog two-dimensional models [2,3]. Thus, a detailed understanding of the transition region in 2D is of relevance to crossovers from weakly to strongly interacting regimes in a wide class of models based on doubly-indexed dynamical variables with symmetry SU(N ).…”

Summing planar diagrams by an integrable bootstrap

“…The asymptotic states of the S matrix, with r or N − r finite, consist only of r = 1 particles and r = N − 1 antiparticles, to any finite order of 1/N. There are, however, bound states of infinite numbers of elementary particles, which correspond to keeping r/N = ρ fixed, as N → ∞ [14]. These bound states of infinitely many particles have mass ≈ Nm 1 (sin ρ)/π, which becomes infinite in the 't Hooft limit, with m 1 fixed.…”