Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models

TL;DR

This paper explores the integrability, quantum behavior, and dualities of Yang-Baxter deformed 2D models with Wess-Zumino terms, revealing a deep link between classical integrability and quantum renormalization.

Contribution

It demonstrates that classical integrability conditions are essential to prevent new couplings during quantum renormalization in these models.

Findings

Classical integrability prevents new couplings from appearing quantum mechanically.

Poisson-Lie T-duality acts as an inversion of coupling constants in these models.

The Wess-Zumino-Witten model is the IR fixed point and self-dual point.

Abstract

We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral Model with a Wess-Zumino term. For arbitrary groups, the one-loop beta functions are calculated and display a surprising connection between classical and quantum physics: the classical integrability condition is necessary to prevent new couplings being generated by renormalisation. We show these theories admit an elegant realisation of Poisson-Lie T-duality acting as a simple inversion of coupling constants. The self-dual point corresponds to the Wess-Zumino-Witten model and is the IR fixed point under RG. We address the possibility of having supersymmetric extensions of these models showing that extended supersymmetry is not possible in general.