Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function

We carry out a high-precision simulation of the two-dimensional $SU(3)$ principal chiral model at correlation lengths $\xi$ up to $\sim 4 \times 10^5$, using a multi-grid Monte Carlo (MGMC) algorithm and approximately one year of Cray C-90 CPU time. We extrapolate the finite-volume Monte Carlo data to infinite volume using finite-size-scaling theory, and we discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to ...

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 describe how an SU(N) chiral gauge theory can be put on the lattice using non-perturbative gauge fixing. In particular, we explain how the Gribov problem is dealt with. Our construction is local, avoids doublers, and weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory.

The strong-coupling character expansion of lattice models is reanalyzed in the perspective of its complete algorithmization. The geometric problem of identifying, counting, and grouping together all possible contributions is disentangled from the group-theoretical problem of weighting them properly. The first problem is completely solved for all spin models admitting a character-like expansion and for arbitrary lattice connectivity. The second problem is reduced to the evalua...

Strong-coupling analysis of two-dimensional chiral models, extended to 15th order, allows for the identification of a scaling region where known continuum results are reproduced with great accuracy, and asymptotic scaling predictions are fulfilled. The properties of the large-$N$ second-order phase transition are quantitatively investigated.

Wilson loops in large N gauge theory exhibit a weak to strong coupling transition as the loop is dilated. A multiplicative matrix model captures the universal behavior associated with this transition. A universal scaling function is obtained in a double scaling limit. Numerical studies show that both large N QCD in three dimensions and the SU(N) principal chiral model in two dimensions are in the same universality class.

We present the details of analyzing an $SU_L(2)\otimes U_R(1)$ chiral theory with multifermion couplings on a lattice. An existence of a possible scaling region in the phase space of multifermion couplings for defining the continuum limit of chiral fermions is advocated. In this scaling region, no spontaneous symmetry breaking occurs; the ``spectator'' fermion $\psi_R(x)$ is a free mode and decoupled; doublers are decoupled as massive Dirac fermions consistently with the $SU_...

The general features of the 1/N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the large-N properties of spin and gauge models possessing the symmetry group $SU(N) \times SU(N)$. An extensive discussion of the known properties of the single-link integral (equivalent to YM_2 and one-dimensional chiral models) includes finit...

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...

We present first-principle lattice study of the two-dimensional SU(N) x SU(N) Principal Chiral Model (PCM) on the cylinder R x S1 with variable compactification length L0 of S1 and with both periodic and ZN-symmetric twisted boundary conditions. For both boundary conditions our numerical results can be interpreted as signatures of a weak crossover or phase transition between the regimes of small and large L0. In particular, at small L0 thermodynamic quantities exhibit nontriv...