Automatic Fine-Tuning in the 2-Flavor Schwinger Model

TL;DR

This paper explores the 2-flavor Schwinger model, revealing how conformal coalescence explains the suppression of isospin breaking effects at low energies, even with small fermion masses.

Contribution

It introduces the concept of conformal coalescence to understand the model's features and demonstrates automatic exponential suppression of isospin breaking effects.

Findings

Isospin breaking effects are exponentially suppressed for small fermion masses.

Conformal coalescence explains disappearance of certain operators in the low-energy limit.

Automatic exponential fine-tuning occurs without explicit parameter adjustments.

Abstract

I discuss the 2-flavor Schwinger model both without and with fermion masses. I argue that the concept 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 $m_f$ and a mass difference $\delta m$, so long as both are small compared to the dynamical gauge boson mass $m=e\sqrt{2/\pi}$, isospin breaking effects 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 low energy theory, this looks like exponential fine-tuning, but it is done automatically by conformal coalescence.