Abstract
We study the even spin \( {\mathcal{W}}_{\infty } \) which is a universal W -algebra for orthosymplectic series of \( \mathcal{W} \)-algebras. We use the results of Fateev and Lukyanov to embed the algebra into \( {\mathcal{W}}_{1+\infty } \). Choosing the generators to be quadratic in those of \( {\mathcal{W}}_{1+\infty } \), we find that the algebra has quadratic operator product expansions. Truncations of the universal algebra include principal DrinfeǏd -Sokolov reductions of BC D series of simple Lie algebras, orthogonal and symplectic cosets as well as orthosymplectic Y -algebras of Gaiotto and Rapčák. Based on explicit calculations we conjecture a complete list of co-dimension 1 truncations of the algebra.
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Procházka, T. On even spin \( {\mathcal{W}}_{\infty } \). J. High Energ. Phys. 2020, 57 (2020). https://doi.org/10.1007/JHEP06(2020)057
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DOI: https://doi.org/10.1007/JHEP06(2020)057