All-loop correlators of integrable $\lambda$-deformed $\sigma$-models

Understand

We compute the 2- and 3-point functions of currents and primary fields of $\lambda$-deformed integrable $\sigma$-models characterized also by an integer $k$.

• Our results apply for any semisimple group $G$, for all values of the deformation parameter $\lambda$ and up to order $1/k$.
• We deduce the OPEs and equal-time commutators of all currents and primaries.
• We derive the currents' Poisson brackets which assume Rajeev's deformation of the canonical structure of the isotropic PCM, the underlying structure of the integrable $\lambda$-deformed $\sigma$-models.