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arXiv · 2111.07924

CFT correlators, ${\cal W}$-algebras and Generalized Catalan Numbers

Robin Karlsson·Manuela Kulaxizi·Gim Seng Ng·Andrei Parnachev·Petar Tadić
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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 ${\cal W}_N$ vacuum blocks, where a suitable generalization of the Catalan numbers plays the main role. Moreover, the ${\cal W}_N$ 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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Robin Karlsson, Manuela Kulaxizi, Gim Seng Ng, Andrei Parnachev, Petar Tadić. 2021-11-15. CFT correlators, ${\cal W}$-algebras and Generalized Catalan Numbers. https://doi.org/10.1007/jhep06(2022)162

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