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

The large-N saddle-point equations for the principal chiral models defined on a d-1 dimensional simplex are derived from the external field problem for unitary integrals. The saddle point equation are studied analytically and numerically in many relevant instances, including d=4 and $d\rightarrow\infty$, with special attention to the critical domain, which is found to correspond to $\beta_c=1/d$ for all d. Related models (chiral chains) are discussed and large-N solutions are...

We study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large $N$ limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the 't Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the pha...

We study $\theta$ dependence of the vacuum energy for the 4d SU(2) pure Yang-Mills theory by lattice numerical simulations. The response of topological excitations to the smearing procedure is investigated in detail, in order to extract topological information from smeared gauge configurations. We determine the first two coefficients in the $\theta$ expansion of the vacuum energy, the topological susceptibility $\chi$ and the first dimensionless coefficient $b_2$, in the cont...

We apply the tensor renormalization group method to the (1+1)-dimensional SU(2) principal chiral model at finite chemical potential with the use of the Gauss-Legendre quadrature to discretize the SU(2) Lie group. The internal energy at vanishing chemical potential $\mu=0$ shows good consistency with the prediction of the strong and weak coupling expansions. This indicates an effectiveness of the Gauss-Legendre quadrature for the partitioning of the SU(2) Lie group. In the fin...

We obtain exact matrix elements of physical operators of the (1+1)-dimensional nonlinear sigma model of an SU(N)-valued bare field, in the 't Hooft limit N goes to infinity. Specifically, all the form factors of the Noether current and the stress-energy-momentum tensor are found with an integrable bootstrap method. These form factors are used to find vacuum expectation values of products of these operators.

We report an analysis of the Anderson transition in an SU(2) model with chiral symmetry. Clear single parameter scaling behaviour is observed. We estimate the critical exponent for the divergence of the localization length to be $\nu=2.72\pm.02$ indicating that the transition belongs to the symplectic universality class.

We study the correlation function of the 2d SU(2) principal chiral model on the lattice. By rewriting the model in terms of Z(2) degrees of freedom coupled to SO(3) vortices we show that the vortices play a crucial role in disordering the correlations at low temperature. Using a series of exact transformations we prove that, if satisfied, certain inequalities between vortex correlations imply exponential fall-off of the correlation function at arbitrarily low temperatures. We...

We study the phase transition in generalized chiral or Stiefel's models using Monte Carlo simulations. These models are characterized by a breakdown of symmetry O(N)/O(N-P). We show that the phase transition is clearly first order for N >= 3 when P=N and P=N-1, contrary to predictions based on the Renormalization Group in 4-\epsilon expansion but in agreement with a recent non perturbative Renormalization Group approach.

Lattice $SU(N)\times SU(N)$ chiral models are analyzed by strong and weak coupling expansions and by numerical simulations. $12^{th}$ order strong coupling series for the free and internal energy are obtained for all $N\geq 6$. Three loop contributions to the internal energy and to the lattice $\beta$-function are evaluated for all $N$ and non-universal corrections to the asymptotic $\Lambda$ parameter are computed in the ``temperature'' and the ``energy'' scheme. Numerical s...

We study analytically the phase diagram of the pure $SU(N)$ lattice gauge theory at finite temperature, and we attempt to estimate the critical deconfinement temperature. We apply large $N$ techniques to the Wilson and to the Heat Kernel action, and we study the resulting models both in the strong coupling and in the weak coupling limits. Using the Heat Kernel action, we establish an interesting connection between the Douglas-Kazakov phase transition of two-dimensional QCD an...