Bi-$\eta$ and bi-$\lambda$ deformations of ${\mathbb{Z}}_4$ permutation supercosets

Abstract

Integrable string sigma models on AdS${}_3$ backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-$\eta$ and bi-$\lambda$ deformations of two classes of ${\mathbb{Z}}_4$ permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS${}_3$ backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-$\lambda$ deformation.

35 pages, published version