'Schwinger Model' on the Fuzzy Sphere

TL;DR

This paper develops a model of spinor fields interacting with gauge fields on a fuzzy sphere, analyzing chiral symmetry and calculating correlation functions to reveal non-invariance of the partition function.

Contribution

It introduces a novel approach to gauge interactions on fuzzy spheres using the gauged Dirac operator and analyzes chiral symmetry breaking in this context.

Findings

Correlation functions do not vanish, indicating chiral symmetry breaking.

The field strength can be expressed solely in terms of Dirac operators.

The model demonstrates non-invariance of the partition function under chiral transformations.

Abstract

In this paper, we construct a model of spinor fields interacting with specific gauge fields on fuzzy sphere and analyze the chiral symmetry of this 'Schwinger model'. In constructing the theory of gauge fields interacting with spinors on fuzzy sphere, we take the approach that the Dirac operator $D_q$ on q-deformed fuzzy sphere $S_{qF}^2$ is the gauged Dirac operator on fuzzy sphere. This introduces interaction between spinors and specific one parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators $D_q$ and $D$ alone. Using the path integral method, we have calculated the $2n-$point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.