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I discuss the 2-flavor Schwinger model both without and with fermion masses.I argue that the concept of "conformal coalescence," in unparticle physics inwhich linear combinations of short distance operators can disappear from thelong-distance theory, makes it easy to understand some puzzling features of themodel with small fermion masses. In particular, I argue that for an averagefermion mass $m_f$ and a mass difference $\delta m$, so long as both are smallcompared to the dynamical gauge boson mass $m=e\sqrt{2/\pi}$, isospin breakingeffects in the low energy theory are exponentially suppressed by powers of$\exp\Bigl(-(m/m_f)^{2/3}\Bigr)$ even if $\delta m\approx m_f$! In the lowenergy theory, this looks like exponential fine-tuning, but it is doneautomatically by conformal coalescence.

Automatic Fine-Tuning in the 2-Flavor Schwinger Model