One-loop renormalizability of all 2-dimensional Poisson–Lie σ-models

We perform a systematic study of the one-loop renormalizability of all Poisson–Lie T-dualizable σ-models with two-dimensional targets. We show that whatever Drinfeld double and whatever matrix of coupling constants we consider the corresponding σ-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.