Automatic Fine-Tuning in the 2-Flavor Schwinger Model

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 $\exp (-(m/m_f{)}^{2/3})$ 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.

arXiv comment8 pages (suggestions of referees incorporated)

References in corpus (6)

• Unparticle Physics
• Functional Integral Approach to the N-Flavor Schwinger Model
• Massless fermions in multi-flavor QED_2
• Multiflavor Massive Schwinger Model With Non-Abelian Bosonization
• Non-perturbative Effects and Unparticle Physics in Generalized Schwinger Models
• Interplay between $SU(N_f)$ chiral symmetry, $U(1{)}_A$ axial anomaly and massless bosons

Cited by in corpus (7)

• Flow-based sampling in the lattice Schwinger model at criticality
• Phase Diagram of the Two-Flavor Schwinger Model at Zero Temperature
• On the question of quark confinement in the Abelian U(1) QED gauge interaction
• Dynamics of quarks and gauge fields in the lowest-energy states in QCD and QED
• Isospin Breaking Effects in the 2-Flavor Schwinger Model
• Chiral and isospin breaking in the two-flavor Schwinger Model
• The Lattice Schwinger Model and Its Quantum Simulation