Classical Yang-Baxter equation from supergravity
I. Bakhmatov (Asia Pacific Center for Theoretical Physics, Postech, Pohang 37673, Korea, Institute of Physics, Kazan Federal University, Kremlevskaya 16a, 420111, Kazan, Russia); Ö. Kelekci (Faculty of Engineering, University of Turkish Aeronautical Association, 06790 Ankara, Turkey); E. Ó Colgáin (Asia Pacific Center for Theoretical Physics, Postech, Pohang 37673, Korea); M. M. Sheikh-Jabbari (School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran)
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 , 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 is the most general -matrix solution. Our work generalizes Yang-Baxter deformations to non-coset spaces and unlocks gravity as a means to classify -matrix solutions to the CYBE.
