Abstract
Chiral higher spin gravity is defined in terms of a strong homotopy algebra of pre-Calabi-Yau type (noncommutative Poisson structure). All structure maps are given by the integrals over the configuration space of concave polygons and the first two maps are related to the (Shoikhet-Tsygan-)Kontsevich Formality. As with the known formality theorems, we prove the A∞-relations via Stokes’ theorem by constructing a closed form and a configuration space whose boundary components lead to the A∞-relations. This gives a new way to formulate higher spin gravities and hints at a construct encompassing the known formality theorems.
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Acknowledgments
We would like to thank the anonymous Referee for making many valuable suggestions to improve the manuscript. The work of E. S. and R. van D. was partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 101002551). A. Sh. gratefully acknowledges the financial support from the São Paulo Research Foundation (FAPESP), grant 2022/13596-8, and the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”.
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ArXiv ePrint: 2312.16573
Also a visiting professor at the Federal University of ABC, Brazil (Alexey Sharapov)
Research Associate of the Fund for Scientific Research — FNRS, Belgium (Evgeny Skvortsov)
Also on leave from Lebedev Institute of Physics. (Evgeny Skvortsov)
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Sharapov, A., Skvortsov, E. & Van Dongen, R. Strong homotopy algebras for chiral higher spin gravity via Stokes theorem. J. High Energ. Phys. 2024, 186 (2024). https://doi.org/10.1007/JHEP06(2024)186
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DOI: https://doi.org/10.1007/JHEP06(2024)186