Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 6, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP06(2022)162
Keywords
AdS-CFT Correspondence; Conformal and W Symmetry; 1/N Expansion
Categories
Funding
- Irish Research Council Laureate Award
- Ussher Fellowship Award
- U.S. DOE [DE-SC00-17660]
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This research investigates the role of Catalan numbers in the Virasoro heavy-heavy-light-light (HHLL) vacuum blocks and HHLL W-N vacuum blocks in two spacetime dimensions. It reveals that these numbers play a crucial role in the generating function equation and the correlation of stress tensor in the latter case.
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 W-N vacuum blocks, where a suitable generalization of the Catalan numbers plays the main role. Moreover, the 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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