Abstract
In two spacetime dimensions the Virasoro heavy-heavy-light-light (HHLL) vacuum block in a certain limit is governed by the Catalan numbers. The equation for their generating function can be generalized to a differential equation which the logarithm of the block satisfies. We show that a similar story holds for the HHLL \( \mathcal{W} \)N vacuum blocks, where a suitable generalization of the Catalan numbers plays the main role. Moreover, the \( \mathcal{W} \)N blocks have the same form as the stress tensor sector of HHLL near lightcone conformal correlators in 2(N − 1) spacetime dimensions. In the latter case the Catalan numbers are generalized to the numbers of linear extensions of certain partially ordered sets.
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Karlsson, R., Kulaxizi, M., Ng, G.S. et al. CFT correlators, \( \mathcal{W} \)-algebras and generalized Catalan numbers. J. High Energ. Phys. 2022, 162 (2022). https://doi.org/10.1007/JHEP06(2022)162
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DOI: https://doi.org/10.1007/JHEP06(2022)162