Classical Yang-Baxter equation from β-supergravity
Ilya Bakhmatov (Kazan Federal University, Institute of Physics, Kremlevskaya 16a, Kazan, 420111, Russia, Asia Pacific Center for Theoretical Physics, Postech, Pohang, 37673, Korea); Edvard Musaev (Kazan Federal University, Institute of Physics, Kremlevskaya 16a, Kazan, 420111, Russia, Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny, 141700, Russia)
Yang-Baxter deformations of superstring σ-models have recently inspired a supergravity solution generating technique. Using the open/closed string map and a Killing bi-vector as a deformation parameter, new solutions can be built, such that the (generalised) supergravity field equations were conjectured to always reduce to the classical Yang-Baxter equation (CYBE) [1]. In this work we provide a proof of this conjecture, using a systematic approach based on the so-called β-supergravity, which is a dynamical theory for the field β mn instead of the NSNS 2-form b mn .