Three-parameter integrable deformation of Z_4 permutation supercosets

Abstract

A three-parameter integrable deformation of ${\mathbb{Z}}_4$ permutation supercosets is constructed. These supercosets are of the form $\hat{F}/F_0$ where $F_0$ is the bosonic diagonal subgroup of the product supergroup $\hat{F}=\hat{G}\times \hat{G}$. They include the AdS${}_3$ $\times$ S${}^3$ and AdS${}_3$ $\times$ S${}^3$ $\times$ S${}^3$ supercosets. This deformation encompasses both the bi-Yang-Baxter deformation of the semi-symmetric space $\sigma$-model on ${\mathbb{Z}}_4$ permutation supercosets and the mixed flux model. Truncating the action at the bosonic level, we show that one recovers the bi-Yang-Baxter deformation of the principal chiral model plus Wess-Zumino term.

25 pages, published version