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arXiv · 1806.02602

Embedding the modified CYBE in Supergravity

Thiago Araujo·Eoin Ó Colgáin·Hossein Yavartanoo
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Abstract

It has recently been demonstrated that the Classical Yang-Baxter Equation (CYBE) emerges from supergravity via the open-closed string map. Thus, given any solution with an isometry group, there exists a deformed solution based on an $r$-matrix solution to the homogeneous CYBE. In this work, we argue that the CYBE emerges exclusively from the NS sector, while the RR sector acts largely as a spectator that supports the spacetimes. Moreover, shifting the dilaton by a constant, one can incorporate $r$-matrix solutions to the modified CYBE, but only for original geometries that are a direct-product of coset spaces. We illustrate our solution generating technique with deformations of $AdS_3 \times S^3 \times M_4$, where $M_4 = T^4$ (K3) and $S^3 \times S^1$, and explicitly construct one and two-parameter (integrable) q-deformations that are solutions to generalised supergravity.

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Thiago Araujo, Eoin Ó Colgáin, Hossein Yavartanoo. 2018-10-22. Embedding the modified CYBE in Supergravity. https://doi.org/10.1140/epjc%2Fs10052-018-6335-6

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