Classical Yang-Baxter Equation from Supergravity

Understand

We promote the open-closed string map, originally formulated by Seiberg \& Witten, to a solution generating prescription in generalized supergravity.

• The approach hinges on a knowledge of an antisymmetric bivector $\Theta$, built from antisymmetric products of Killing vectors, which is specified by the equations of motion.
• In the cases we study, the equations of motion reproduce the Classical Yang-Baxter equation (CYBE) and $\Theta$ is the most general $r$-matrix solution.
• Our work generalizes Yang-Baxter deformations to non-coset spaces and unlocks gravity as a means to classify $r$-matrix solutions to the CYBE.