Accidental Symmetries and N=1 Duality in Supersymmetric Gauge Theory

TL;DR

This paper explores how accidental symmetries in supersymmetric gauge theories lead to infinite families of dual theories with identical infrared behavior, revealing complex symmetry transformations and potential new fixed points.

Contribution

It demonstrates the existence of continuous sets of dual theories with different ultraviolet descriptions but the same infrared physics, involving non-perturbative interactions and symmetry transformations.

Findings

Infinite dual theory families with identical IR behavior.

Non-perturbative dynamics induce symmetry transformations.

Potential new chiral fixed points and dangerously irrelevant operators.

Abstract

We note that the accidental symmetries which are present in some examples of duality imply the existence of continuously infinite sets of theories with the same infrared behavior. These sets interpolate between theories of different flavors and colors; the change in color and flavor is compensated by interactions (often non-perturbative) induced by operators in the superpotential. As an example we study the behavior of SU(2) gauge theories with 2\nf doublets; these are dual to SU(\nf-2) gauge theories whose ultraviolet flavor symmetry is SU(\nf)xSU(\nf)xU(1) but whose flavor symmetry is SU(2\nf) in the infrared. The infrared SU(2\nf) flavor symmetry is implemented in the ultraviolet as a non-trivial transformation on the Lagrangian and matter content of the magnetic theory, involving (generally non-renormalizable) baryon operators and non-perturbative dynamics. We discuss various implications of this fact, including possible new chiral fixed points and interesting examples of dangerously irrelevant operators.