Highly nonlinear wave solutions in a dual to the chiral model

TL;DR

This paper explores a dual scalar field theory with nilpotent current algebra, revealing classical wave solutions with unique dispersion relations and proposing it as a toy model for understanding strongly coupled quantum field theories.

Contribution

It introduces a dual to the chiral model with a nilpotent current algebra, finds classical wave solutions, and quantizes them, highlighting novel dispersion relations and potential preon-like excitations.

Findings

Classical wave solutions with dispersion rac{2}{3}

Quantization via collective variables

Potential preon-like excitations at strong coupling

Abstract

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 that survive the strong coupling limit and quantize them by the collective variable method. They describe excitations with an unusual dispersion relation $\omega\propto|k|^{\frac{2}{3}}$ . Perhaps they are the "preons" at strong coupling, whose bound states form massless particles over long distances.