Quantum Spin Formulation of the Principal Chiral Model

In the quantum path integral formulation of a field theory model an anomaly arises when the functional measure is not invariant under a symmetry transformation of the Lagrangian. In this paper, generalizing previous work done on the point particle, we show that even at the classical level we can give a path integral formulation for any field theory model. Since classical mechanics cannot be affected by anomalies, the measure of the classical path integral of a field theory mu...

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.

We study the twisted Eguchi-Kawai (TEK) reduction procedure for large-N unitary matrix lattice models. In particular, we consider the case of two-dimensional principal chiral models, and use numerical Monte Carlo (MC) simulations to check the conjectured equivalence of TEK reduced model and standard lattice model in the large-N limit. The MC results are compared with the large-N limit of lattice principal chiral models to verify the supposed equivalence. The consistency of th...

We derive, in path integral approach, the (anomalous) master Ward identity associated with an infinite set of nonlocal conservation laws in two-dimensional principal chiral models

A novel classically integrable model is proposed. It is a deformation of the two-dimensional principal chiral model, embedded into a heterotic $\sigma$-model, by a particular heterotic gauge field. This is inspired by the bosonic part of the heterotic $\sigma$-model and its recent Hamiltonian formulation in terms of O$(d,d+n)$-generalised geometry by Hatsuda, Mori, Sasaki and Yata. Classical integrability is shown by construction of a Lax pair and a classical $\mathcal{R}$-ma...

We consider a two-dimensional scalar field theory with a nilpotent current algebra, which is dual to the Principal Chiral Model. The quantum theory is renormalizable and not asymptotically free: the theory is strongly coupled at short distances (encountering a Landau pole). We suggest it can serve as a toy model for $\lambda\phi^{4}$ theory in four dimensions, just as the principal chiral model is a useful toy model for Yang-Mills theory. We find some classical wave solutions...

Path integration over Euclidean chiral fermions is replaced by the quantum mechanics of an auxiliary system of non--interacting fermions. Our construction avoids the no--go theorem and faithfully maintains all the known important features of chiral fermions, including the violation of some perturbative conservation laws by gauge field configurations of non--trivial topology.

An anomaly-free quantum theory of a relativistic string is constructed in two-dimensional space-time. The states of the string are found to be similar to the states of a massless chiral quantum particle. This result is obtained by generalizing the concept of an ``operator'' in quantum field theory.

The properties of (N X N)-matrix-valued-field theories, in the limit N goes to infinity, are harder to obtain than those for isovector-valued field theories. This is because we know less about the sum of planar diagrams than the sum of bubble/linear diagrams. Combining the 1/N-expansion with the axioms for form factors, exact form factors can be found for the integrable field theory of an SU(N)-valued field in 1+1 dimensions. These form factors can be used to find the vacuum ...

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.