Non-Abelian BFFT embedding, Schr\"odinger quantization and the anomaly of the O(N) nonlinear sigma model

TL;DR

This paper embeds the O(N) nonlinear sigma model into a non-Abelian gauge framework, quantizes it via Schr"odinger and BV methods, and reveals quantum anomalies breaking classical gauge symmetries.

Contribution

It introduces a novel non-Abelian embedding of the sigma model and analyzes quantum anomalies using two distinct quantization approaches.

Findings

Wave functionals for ground and excited states obtained for N=2

Quantum anomalies detected at one-loop level

Classical gauge symmetries broken quantum mechanically

Abstract

We embed the O(N) nonlinear sigma model in a non-Abelian gauge theory. As a first class system, it is quantized using two different approaches: the functional Schr\"odinger method and the non-local field-antifield procedure. Firstly, the quantization is performed with the functional Schr\"{o}dinger method, for N=2, obtaining the wave functionals for the ground and excited states. In the second place, using the BV formalism we compute the one-loop anomaly. This important result shows that the classical gauge symmetries, appearing due to the conversion via BFFT method, are broken at the quantum level.