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Classical Yang-Baxter Equation from Supergravity · arXivDesk

1710.06784Oct 18, 20176 pages, double column; v2 Schwarzschild example improved, thereby demonstrating that Yang-Baxter deformations can be extended to non-coset geometries

Classical Yang-Baxter Equation from Supergravity

I. Bakhmatov, Ö. Kelekci, E. Ó Colgáin, M. M. Sheikh-Jabbari

Theory

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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 $Θ$ , 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 $Θ$ 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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Researchers working in hep-th and adjacent areas.

Claims

The paper addresses: Classical Yang-Baxter Equation from Supergravity.
We promote the open-closed string map, originally formulated by Seiberg & Witten, to a solution generating prescription in generalized supergravity.

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Author comment: 6 pages, double column; v2 Schwarzschild example improved, thereby demonstrating that Yang-Baxter deformations can be extended to non-coset geometries