• DOI:10.1103/PhysRevLett.117.071602
• Corpus ID: 1290123

Superintegrability of d-Dimensional Conformal Blocks.

@article{Isachenkov2016SuperintegrabilityOD,
  title={Superintegrability of d-Dimensional Conformal Blocks.},
  author={Mikhail Isachenkov and Volker Schomerus},
  journal={Physical review letters},
  year={2016},
  volume={117 7},
  pages={
          071602
        }
}

• Mikhail Isachenkov, V. Schomerus
• Published 4 February 2016
• Mathematics, Physics
• Physical review letters

We observe that conformal blocks of scalar four-point functions in a d-dimensional conformal field theory can be mapped to eigenfunctions of a two-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. We conclude with a short outlook, in particular, on the consequences of integrability for the theory of conformal blocks.