Embedding the modified CYBE in supergravity

It has recently been demonstrated that given a generic solution, the Classical Yang–Baxter Equation (CYBE) emerges from supergravity via the open-closed string map, thus providing tangible evidence for the conjectured equivalence between supergravity equations of motion and the homogeneous CYBE. To date, study of this equivalence has largely been confined to the NS sector. In this work, we make two extensions. First, we revisit the transformation of the RR sector and clarify its precise role in the emergence of the CYBE. Secondly, we identify direct products of coset geometries as the only setting where the transformation permits embeddings of the modified CYBE. We illustrate our solution generating technique with deformations of AdS₃× S³× M₄, where M₄= T⁴ (K3) and S³× S¹, and explicitly construct one and two-parameter integrable q-deformations that are solutions to generalised supergravity.