Classical Yang-Baxter equation from supergravity

Abstract

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 $\mathrm{\ensuremath{\Theta}}$, 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 $\mathrm{\ensuremath{\Theta}}$ 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.