Self-duality in quantum impurity problems

TL;DR

This paper uncovers an exact self-duality in quantum impurity problems, linking different particle descriptions and revealing deep mathematical structures similar to those in supersymmetric gauge theories.

Contribution

It demonstrates a non-perturbative self-duality in quantum impurity models like Luttinger liquids, connecting electron and quasiparticle descriptions.

Findings

Self-duality exists in Luttinger liquids with impurities.

Duality relates electrons to Laughlin quasiparticles.

Mathematical structure resembles supersymmetric gauge theories.

Abstract

We establish the existence of an exact non-perturbative self-duality in a variety of quantum impurity problems, including the Luttinger liquid or quantum wire with impurity. The former is realized in the fractional quantum Hall effect, where the duality interchanges electrons with Laughlin quasiparticles. We discuss the mathematical structure underlying this property, which bears an intriguing resemblance with the work of Seiberg and Witten on supersymmetric non-abelian gauge theory.