Abstract
We show that there are four chiral \( \mathcal{W} \)-algebra extensions of \( \mathfrak{so}\left(2,3\right) \) algebra and construct them explicitly. We do this by a simple identification of each of the inequivalent embeddings of a copy of \( \mathfrak{sl}\left(2,\mathbb{R}\right) \) in the \( \mathfrak{so}\left(2,3\right) \) algebra and the maximal subalgebra \( \mathfrak{h} \) that commutes with it. Then using the standard 2d chiral CFT techniques we find the corresponding \( \mathcal{W} \)-algebra extensions. Two of the four resultant \( \mathcal{W} \)-algebras are new, one of which may be thought of as the conformal \( {\mathfrak{bms}}_3 \) algebra valid for finite values of its central charge.
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Acknowledgments
We thank Suresh Govindarajan, Bala Sathiapalan and Adarsh Sudhakar for helpful conversations. Thanks are also due to the participants of the 5th edition of Chennai Strings Meeting (February 2023) for helpful comments on parts of this work presented there.
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Gupta, N., Suryanarayana, N.V. All chiral \( \mathcal{W} \)-algebra extensions of \( \mathfrak{so}\left(2,3\right) \). J. High Energ. Phys. 2024, 137 (2024). https://doi.org/10.1007/JHEP08(2024)137
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DOI: https://doi.org/10.1007/JHEP08(2024)137