CFT correlators, ${\cal W}$-algebras and Generalized Catalan Numbers
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 vacuum blocks, where a suitable generalization of the Catalan numbers plays the main role. Moreover, the blocks have the same form as the stress tensor sector of HHLL near lightcone conformal correlators in spacetime dimensions. In the latter case the Catalan numbers are generalized to the numbers of linear extensions of certain partially ordered sets.
Cite
@article{arxiv.2111.07924,
title = {CFT correlators, ${\cal W}$-algebras and Generalized Catalan Numbers},
author = {Robin Karlsson and Manuela Kulaxizi and Gim Seng Ng and Andrei Parnachev and Petar Tadić},
journal= {arXiv preprint arXiv:2111.07924},
year = {2022}
}
Comments
36 pages, 6 figures. v2: Minor correction of reference. v3: Minor clarifications and one added reference