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arXiv · 2105.00021

Gaudin Models and Multipoint Conformal Blocks: General Theory

Ilija Buric·Sylvain Lacroix·Jeremy Mann·Lorenzo Quintavalle·Volker Schomerus
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Abstract

The construction of conformal blocks for the analysis of multipoint correlation functions with $N > 4$ local field insertions is an important open problem in higher dimensional conformal field theory. This is the first in a series of papers in which we address this challenge, following and extending our short announcement in [Phys. Rev. Lett. 126, 021602]. According to Dolan and Osborn, conformal blocks can be determined from the set of differential eigenvalue equations that they satisfy. We construct a complete set of commuting differential operators that characterize multipoint conformal blocks for any number $N$ of points in any dimension and for any choice of OPE channel through the relation with Gaudin integrable models we uncovered in [Phys. Rev. Lett. 126, 021602]. For 5-point conformal blocks, there exist five such operators which are worked out smoothly in the dimension $d$.

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Ilija Buric, Sylvain Lacroix, Jeremy Mann, Lorenzo Quintavalle, Volker Schomerus. 2021-04-30. Gaudin Models and Multipoint Conformal Blocks: General Theory. https://doi.org/10.1007/jhep10(2021)139

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