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arXiv · 1602.01858

Superintegrability of $d$-dimensional Conformal Blocks

Mikhail Isachenkov·Volker Schomerus
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Abstract

We observe that conformal blocks of scalar 4-point functions in a $d$-dimensional conformal field theory can mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled Pöschl-Teller particles. Their interaction, whose strength depends smoothly on the dimension $d$, is known to be superintegrable. Our observation enables us to exploit the rich mathematical literature on Calogero-Sutherland models in deriving various results for conformal field theory. These include an explicit construction of conformal blocks in terms of Heckman-Opdam hypergeometric functions and a remarkable duality that relates the blocks of theories in different dimensions.

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Mikhail Isachenkov, Volker Schomerus. 2016-02-04. Superintegrability of $d$-dimensional Conformal Blocks. https://doi.org/10.1103/physrevlett.117.071602

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