Topological Susceptibility and Contact Term in QCD. A Toy Model

TL;DR

The paper addresses how θ-dependence and a non-dispersive, wrong-sign contact term saturate the topological susceptibility in gauge theories, illuminating the U(1)A problem. It develops a center-stabilized, deformed QCD that remains confining and analytically tractable, enabling a controlled study of topological sectors and tunneling phenomena. The authors map a three-dimensional monopole gas to a multi-component sine-Gordon theory to derive a finite, non-dispersive χ in the pure gauge case and show that introducing massless quarks yields χ(m_q=0)=0 through η'–gluon dynamics, consistent with Ward identities. The work connects these results to the Veneziano ghost framework and lattice findings, and discusses broader implications for finite-volume effects and potential Casimir-type corrections relevant to cosmology.

Abstract

We study a number of different ingredients related to $θ$ 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.