Yang-Baxter deformations of $W_{2,4}\times T^{1,1}$ and the associated T-dual models

TL;DR

This paper investigates Yang-Baxter deformations of a specific string theory background and confirms a conjecture relating these deformations to non-abelian T-dualities, even in non-integrable cases.

Contribution

It provides evidence that the conjecture linking Yang-Baxter deformations to T-dualities holds beyond integrable models, demonstrated through the $W_{2,4} imes T^{1,1}$ background.

Findings

Yang-Baxter deformations are equivalent to non-abelian T-dualities for this background.

The conjecture applies to non-symmetric, non-integrable cases.

Supports the conjecture's validity beyond integrable models.

Abstract

Recently, for principal chiral models and symmetric coset sigma models, Hoare and Tseytlin proposed an interesting conjecture that the Yang-Baxter deformations with the homogeneous classical Yang-Baxter equation are equivalent to non-abelian T-dualities with topological terms. It is significant to examine this conjecture for non-symmetric (i.e., non-integrable) cases. Such an example is the $W_{2,4}\times T^{1,1}$ background. In this note, we study Yang-Baxter deformations of type IIB string theory defined on $W_{2,4}\times T^{1,1}$ and the associated T-dual models, and show that this conjecture is valid even for this case. Our result indicates that the conjecture would be valid beyond integrability.