Remarks on Axion-like models
  For a recently proposed alternative to the traditional axion model, we study its long distance behavior, in particular the confinement versus screening issue, and show that a compactified version of this theory can be further mapped into the massive Schwinger model. Our calculation is based on the gauge-invariant but path-dependent variables formalism. This result agrees qualitatively with the usual axion model. 
Patricio Gaete and Iv\'an Schmidt