Embedding the modified CYBE in Supergravity

TL;DR

This paper explores how the classical and modified CYBE relate to supergravity solutions, showing that the CYBE originates from the NS sector and enabling the construction of deformed supergravity backgrounds using $r$-matrices.

Contribution

It demonstrates that the CYBE emerges solely from the NS sector and extends the solution-generating technique to include modified CYBE deformations for coset space geometries.

Findings

CYBE arises exclusively from the NS sector.

Deformations can be constructed for coset space geometries.

Explicit examples include deformations of $AdS_3 imes S^3 imes M_4$.

Abstract

It has recently been demonstrated that the Classical Yang-Baxter Equation (CYBE) emerges from supergravity via the open-closed string map. Thus, given any solution with an isometry group, there exists a deformed solution based on an $r$-matrix solution to the homogeneous CYBE. In this work, we argue that the CYBE emerges exclusively from the NS sector, while the RR sector acts largely as a spectator that supports the spacetimes. Moreover, shifting the dilaton by a constant, one can incorporate $r$-matrix solutions to the modified CYBE, but only for original geometries that are a direct-product of coset spaces. We illustrate our solution generating technique with deformations of $AdS_3 \times S^3 \times M_4$, where $M_4 = T^4$ (K3) and $S^3 \times S^1$, and explicitly construct one and two-parameter (integrable) q-deformations that are solutions to generalised supergravity.