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.
Highlights
Generating exact solutions to gravity theories is a fine, but well-practiced art [1,2]
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
We provide the first example of a gravitational set-up with an innate knowledge of the CYBE
Summary
Generating exact solutions to gravity theories is a fine, but well-practiced art [1,2]. Its connection to T-duality has been exploited in actions that make nongeometric fluxes manifest [23,24] and string theory explanations [25,26] of the Ω-deformation [27,28] It was noted [29,30] that the closed-open string map undoes integrable deformations of σ-models [14,15,16,17]. Starting from a supergravity solution with metric G and zero NSNS two-form, or B-field, one turns on an antisymmetric bivector Θ This defines “open string data,” which upon inverting a single matrix, generates “closed string data,” namely a new metric g and B-field. We provide the first example of a gravitational set-up with an innate knowledge of the CYBE
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