Asymmetric $\lambda$-deformed cosets

TL;DR

This paper investigates integrable asymmetric lambda-deformations of certain coset models, constructs their geometries, and discovers a Z2 symmetry linking asymmetric and symmetric deformations.

Contribution

It provides a systematic construction of deformed geometries for asymmetric lambda-deformations and reveals a Z2 transformation connecting asymmetric and symmetric models.

Findings

Constructed all deformed geometries inductively.

Discovered a Z2 transformation linking asymmetric and symmetric models.

Enhanced understanding of integrable deformations in coset models.

Abstract

We study the integrable asymmetric $\lambda$-deformations of the $SO(n+1)/SO(n)$ coset models, following the prescription proposed in \cite{AsyLambda}. We construct all corresponding deformed geometries in an inductive way. Remarkably we find a $Z_2$ transformation which maps the asymmetric $\lambda$--deformed models to the symmetric $\lambda$--deformed models.