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2018

Classical Yang-Baxter equation from beta-supergravity

Bakhmatov, Ilya, Musaev, Edvard

Understand

Yang-Baxter deformations of superstring sigma-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).
In this work we provide a proof of this conjecture, using a systematic approach based on the so-called $\beta$-supergravity, which is a dynamical theory for the field $\beta^{mn}$ instead of the NSNS 2-form $b_{mn}$.