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

TL;DR

This paper constructs bi-$ heta$ and bi-$eta$ deformations of $ ext{AdS}_3$ supercoset sigma models, exploring their integrability, supergravity backgrounds, and quantum properties, including two-loop RG flow analysis.

Contribution

It introduces new bi-deformation models for $ ext{AdS}_3$ supercosets, analyzing their classical integrability and quantum RG flow behavior.

Findings

Deformed supergravity backgrounds likely preserve 8 supersymmetries.

Two-loop RG flow of bosonic truncation studied.

Models exhibit rich deformation structure due to supergroup product.

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.