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arXiv · 1910.07997

On even spin $W_\infty$

Tomáš Procházka
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Abstract

We study the even spin $\mathcal{W}_\infty$ which is a universal $\mathcal{W}$-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 Drinfeľd-Sokolov reductions of $BCD$ 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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Tomáš Procházka. 2019-10-17. On even spin $W_\infty$. https://doi.org/10.1007/jhep06(2020)057

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