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

TL;DR

This paper computes all-loop 2- and 3-point correlation functions of currents and primary fields in integrable ${ extlambda}$-deformed ${ extsigma}$-models, revealing their operator product expansions, commutators, and Poisson brackets for various limits.

Contribution

It provides explicit all-loop correlation functions and algebraic structures for ${ extlambda}$-deformed ${ extsigma}$-models, including special limits like non-Abelian T-duality and pseudodual models.

Findings

Derived 2- and 3-point functions for currents and primaries.

Established OPEs and equal-time commutators.

Presented Poisson brackets consistent with Rajeev's deformation.

Abstract

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. We also present analogous results in two limiting cases of special interest, namely for the non-Abelian T-dual of the PCM and for the pseudodual model.