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arXiv · 1710.06784

Classical Yang-Baxter Equation from Supergravity

I. Bakhmatov·Ö. Kelekci·E. Ó Colgáin·M. M. Sheikh-Jabbari
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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 $\Theta$, 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.

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I. Bakhmatov, Ö. Kelekci, E. Ó Colgáin, M. M. Sheikh-Jabbari. 2017-10-18. Classical Yang-Baxter Equation from Supergravity. https://doi.org/10.1103/physrevd.98.021901

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