Abstract
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 βmn instead of the NSNS 2-form bmn.
Highlights
The map (1.1) was originally introduced by Seiberg and Witten [6] in their seminal study of open strings on D-branes in the background fields gmn, bmn, which belong to the closed string spectrum
Assuming the classical Yang-Baxter equation (CYBE) for the deformation parameter it was proven that kappa-symmetry is preserved under the deformation, which implies that the background fields satisfy the supergravity field equations [25]
The above calculations provide a proof of the conjecture of [1]: we have shown that the classical Yang-Baxter equation emerges from the open/closed string map, applied to supergravity solutions deformed by a 2-form (2.14), assuming that we do not have to deal with generalised supergravity ∇mβmn = 0
Summary
The map (1.1) was originally introduced by Seiberg and Witten [6] in their seminal study of open strings on D-branes in the background fields gmn, bmn, which belong to the closed string spectrum. 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]. The DFT construction implies that the background gmn, bmn, φ resulting from the open/closed string map is a solution to the standard b-frame supergravity field equations.
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