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arXiv · 2007.15965

Automatic Fine-Tuning in the 2-Flavor Schwinger Model

Howard Georgi
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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.

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Howard Georgi. 2020-07-31. Automatic Fine-Tuning in the 2-Flavor Schwinger Model. https://doi.org/10.1103/physrevlett.125.181601

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