Topological Susceptibility and Contact Term in QCD. A Toy Model

TL;DR

This paper investigates topological effects and the U(1)_A problem in QCD using a simplified, weakly coupled model called deformed QCD, providing insights into complex nonperturbative phenomena.

Contribution

It introduces a toy model that captures essential QCD features, allowing explicit analysis of topological susceptibility and contact terms related to the U(1)_A problem.

Findings

Explicit demonstration of topological susceptibility with the correct sign.

Insights into the microscopic origin of contact terms in gauge theories.

Validation of theoretical ideas about the U(1)_A problem in a controllable setting.

Abstract

We study a number of different ingredients related to $\theta$ dependence, the non-dispersive contribution in topological susceptibility with the "wrong" sign, topological sectors in gauge theories, and related subjects using a simple "deformed QCD". This model is a weakly coupled gauge theory, which however has all the relevant essential elements allowing us to study difficult and nontrivial questions which are known to be present in real strongly coupled QCD. Essentially we want to test the ideas related to the $U(1)_A$ problem in a theoretically controllable manner using the "deformed QCD" as a toy model. One can explicitly see microscopically how the crucial elements work.