Automatic Fine-Tuning in the Two-Flavor Schwinger Model

Abstract

I discuss the two-flavor Schwinger model both without and with fermion masses. I argue that the phenomenon of "conformal coalescence,"in unparticle physics in which linear combinations of short-distance operators can disappear from the long-distance theory, makes it easy to understand some puzzling features of the model with small fermion masses. In particular, I argue that for an average fermion mass mf and a mass difference δm, so long as both are small compared to the dynamical gauge boson mass m=e2/π, isospin-breaking effects in the low-energy theory are exponentially suppressed by powers of exp[-(m/mf)2/3] even if δm≈mf. In the low-energy theory, this looks like exponential fine-tuning, but it is done automatically by conformal coalescence.