Superintegrability of d-Dimensional Conformal Blocks.

  title={Superintegrability of d-Dimensional Conformal Blocks.},
  author={Mikhail Isachenkov and Volker Schomerus},
  journal={Physical review letters},
  volume={117 7},
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… 
Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
Conformal blocks are the central ingredient of the conformal bootstrap programme. We elaborate on our recent observation that uncovered a relation with wave functions of an integrable
Gaudin models and multipoint cnformal blocks: general theory
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
Thermal conformal blocks
We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second-order Casimir differential
Dimensional reduction for conformal blocks
A bstractWe consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d + 1, 1) up into multiplets of SO(d, 1). This leads to an expansion of
From Gaudin Integrable Models to d-Dimensional Multipoint Conformal Blocks.
The main observation is that conformal blocks for N-point functions may be considered as eigenfunctions of integrable Gaudin Hamiltonians, which provides a complete set of differential equations that can be used to evaluate multipoint blocks.
On conformal blocks, crossing kernels and multi-variable hypergeometric functions
Abstract In this note, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
A bstractConformal blocks are the central ingredient of the conformal bootstrap programme. We elaborate on our recent observation that uncovered a relation with wave functions of an integrable
Quantum integrable systems from conformal blocks
In this note, we extend the striking connections between quantum integrable systems and conformal blocks recently found in this http URL in several directions. First, we explicitly demonstrate that
From spinning conformal blocks to matrix Calogero-Sutherland models
A bstractIn this paper we develop further the relation between conformal four-point blocks involving external spinning fields and Calogero-Sutherland quantum mechanics with matrix-valued potentials.
Dimensional reduction of higher-point conformal blocks
Recently, with the help of Parisi-Sourlas supersymmetry an intriguing relation was found expressing the four-point scalar conformal block of a (d-2)-dimensional CFT in terms of a five-term linear


Theory of Hypergeometric Functions
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
  • Phys. B678, 491
  • 2004
Transformation Groups 10
  • 63
  • 2005
Annals Phys
  • 76, 161
  • 1973
  • Rept. 94, 313
  • 1983
Scholarpedia 7
  • 7761
  • 2012