Bosonic $\eta$-deformations of Non-integrable Backgrounds

TL;DR

This paper constructs integrable bosonic $ ext{eta}$-deformations of non-integrable backgrounds $W_{2,4} imes T^{1,1}$ and $AdS_5 imes T^{1,1}$ using an $r$-matrix approach, expanding the landscape of integrable string backgrounds.

Contribution

It introduces a method to derive integrable $ ext{eta}$-deformations of non-integrable backgrounds via solutions to the modified Yang-Baxter equation.

Findings

Derived new integrable deformed backgrounds from non-integrable ones.

Established a link between $r$-matrix solutions and background integrability.

Expanded the class of known integrable string theory backgrounds.

Abstract

We consider the non-integrable bosonic backgrounds $W_{2,4}\times T^{1,1}$ and $AdS_5\times T^{1,1}$ and derive their bosonic $\eta$-deformed versions using an $r$-matrix that solves the modified Yang-Baxter equation obtaining new integrable deformed backgrounds.