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

We discuss how the $1/N_c$ expansion and the chiral random matrix theory ($\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid: while the fermion mass $m$ is fixed in the standard large-$N_c$ arguments ('t Hooft large-$N_c$ limit), $m$ must be scaled appropriately with a certain negative power of $N_c$ in order for the gauge theories to be described by the $\chi$RMT. Then, altho...

We analyze the dynamics of an $SU_L(2)\otimes U_R(1)$ chiral gauge theory on a lattice with a large multifermion coupling $1\ll g_2 < \infty$. It is shown that no spontaneous symmetry breaking occurs; the ``spectator'' fermion $\psi_R(x)$ is a free mode; doublers are decoupled as massive Dirac fermions consistently with the chiral gauge symmetry. Whether right-handed three-fermion states disappear and chiral fermions emerge in the low-energy limit are discussed. Provided righ...

The main technical and conceptual features of the lattice $1/N$ expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$ $\sigma$ models, with standard and improved lattice actions. We show how to perform the asymptotic expansion of effective propagators for small values of the mass gap and how to employ this result in the evaluation of physical quantities in the scaling regime. The...

We carry out a high-precision simulation of the two-dimensional $SU(3)$ principal chiral model at correlation lengths $\xi$ up to $\approx\! 4 \times 10^5$, using a multi-grid Monte Carlo (MGMC) algorithm. 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 the renormalization-group predictions. For $...

In this paper we study the ground state properties of a ladder Hamiltonian with chiral $SU(2)$-invariant spin interactions, a possible first step towards the construction of truly two dimensional non-trivial systems with chiral properties starting from quasi-one dimensional ones. Our analysis uses a recent implementation by us of $SU(2)$ symmetry in tensor network algorithms, specifically for infinite Density Matrix Renormalization Group (iDMRG). After a preliminary analysis ...

As a non-perturbative and gauge invariant regularization the lattice provides a tool for deeper understanding of the celebrated Yang-Mills theory, QCD and chiral gauge theories. For illustration, I discuss some analytic developments on the lattice related to chiral symmetry, chiral fermions and improvement programs. Chiral symmetry on the lattice has an amazing history, and it might influence our perception of a symmetry beyond this example.

Principal chiral models on a d-1 dimensional simplex are introduced and studied analytically in the large $N$ limit. The $d = 0, 2, 4$ and $\infty$ models are explicitly solved. Relationship with standard lattice models and with few-matrix systems in the double scaling limit are discussed.

Albeit the standard model is the most successful model of particles physics, it still has some theoretical shortcomings, for instance the hierarchy problem, the absence of dark matter, etc. Supersymmetric extensions of the standard model could be a possible solution to these problems. One of the building blocks of these supersymmetric models are supersymmetric gauge theories. It is expected that they exhibit interesting features like confinement, chiral symmetry breaking, mag...

In this work we study the critical behavior and momentum dependence of chirality-flipping fermion 4-point functions in non-abelian gauge theories. Our formalism is based on the Schwinger-Dyson system of equations. Considering the large-N limit of an SU(N) theory simplifies the problem considerably, showing us clearly which Green functions can be non-zero and which not. It also allows us to draw conclusions on chirality-flipping n-point functions for n larger than four.

A new block spin renormalization group transformation for SU(N) gauge models is proposed near the non-trivial fixed point in perturbation theory and thereby the expectation values of various Wilson loops on the renormalized trajectory near the fixed point are explicitly obtained. An improved action is obtained as in a preceding paper and a criterion for the scaling behavior of physical quantities is also given.