Instantons in QCD contribute to the up, down, and strange quark masses (see, e.g., Georgi and McArthur (1981) or Kaplan and Manohar (1986)). Some papers claim that this contribution is equivalent to additive renormalization (see, e.g., Banks, Nir, Seiberg (1994) or Creutz (2004)). Is this statement really true?
If the contribution is due to instantons, then it should affect both the up and down quark masses, and it could not vanish in the isospin limit $m_u=m_d$. However, Creutz (2004) argues that the contribution vanishes for $m_u=m_d$, based on additive renormalization arguments. How are these two arguments consistent with each other?
Moreover, there are theories like the Schwinger model (QED in 1+1 dimensions), which contain instantons and are super-renormalizable, so additive renormalization should not exist there. Does the instanton contribution to the fermion mass exist in such a model? If so, how does it look like?