One-loop renormalizability of all 2d dimensional Poisson-Lie sigma-models

TL;DR

This paper proves that all 2D Poisson-Lie sigma-models are one-loop renormalizable and that their RG flows respect Poisson-Lie T-duality, regardless of the Drinfeld double or coupling matrices.

Contribution

It establishes the universal one-loop renormalizability of all 2D Poisson-Lie sigma-models and confirms the compatibility of RG flows with T-duality.

Findings

All models are one-loop renormalizable.

RG flows are compatible with Poisson-Lie T-duality.

Renormalizability holds for any Drinfeld double and coupling matrix.

Abstract

We perform a systematic study of the one-loop renormalizability of all Poisson-Lie T-dualizable $\si$-models with two-dimensional targets. We show that whatever Drinfeld double and whatever matrix of coupling constants we consider the corresponding $\si$-model is always one-loop renormalizable in the strict field theoretical sense. Moreover, in all cases, the RG flow in the space of the coupling constants is compatible with the Poisson-Lie T-duality.