Quantum Mechanically Induced Wess-Zumino Term in the Principal Chiral Model

TL;DR

This paper demonstrates that the Wess-Zumino term can be generated quantum mechanically in the two-dimensional principal chiral model, transforming it into the Wess-Zumino-Novikov-Witten model at a specific coupling, through hidden topological effects.

Contribution

It reveals that the Wess-Zumino term arises from inequivalent quantizations on a sphere in the model's configuration space, linking monopole potentials to the Wess-Zumino term.

Findings

Wess-Zumino term can be induced quantum mechanically in the model.

The induced term transforms the model into the Wess-Zumino-Novikov-Witten model.

Dirac monopole potential is identified as the Wess-Zumino term.

Abstract

It is argued that, in the two dimensional principal chiral model, the Wess-Zumino term can be induced quantum mechanically, allowing the model with the critical value of the coupling constant $\lambda^2 = 8\pi/|k|$ to turn into the Wess-Zumino-Novikov-Witten model at the quantum level. The Wess-Zumino term emerges from the inequivalent quantizations possible on a sphere hidden in the configuration space of the original model. It is shown that the Dirac monopole potential, which is induced on the sphere in the inequivalent quantizations, turns out to be the Wess-Zumino term in the entire configuration space.