Remarks on confinement driven by axion-like particles in Yang-Mills theories

Features of screening and confinement are studied for a non-Abelian gauge theory with a mixture of pseudoscalar and scalar coupling, in the case where a constant chromo-electric, or chromo-magnetic, strength expectation value is present. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism. We explicitly show that the static potential profile is the sum of a Yukawa and a linear potential, leading to the confinement of static probe charges. Interestingly, similar results have been obtained in the context of gluodynamics in curved space-time. For only pseudoscalar coupling, the results are radically different.