Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 007, 38 pages      arXiv:2009.00393      https://doi.org/10.3842/SIGMA.2021.007
Contribution to the Special Issue on Representation Theory and Integrable Systems in honor of Vitaly Tarasov on the 60th birthday and Alexander Varchenko on the 70th birthday

Harmonic Analysis in $d$-Dimensional Superconformal Field Theory

Ilija Burić
DESY, Notkestraße 85, D-22607 Hamburg, Germany

Received September 02, 2020, in final form January 15, 2021; Published online January 25, 2021

Abstract
Superconformal blocks and crossing symmetry equations are among central ingredients in any superconformal field theory. We review the approach to these objects rooted in harmonic analysis on the superconformal group that was put forward in [J. High Energy Phys. 2020 (2020), no. 1, 159, 40 pages, arXiv:1904.04852] and [J. High Energy Phys. 2020 (2020), no. 10, 147, 44 pages, arXiv:2005.13547]. After lifting conformal four-point functions to functions on the superconformal group, we explain how to obtain compact expressions for crossing constraints and Casimir equations. The later allow to write superconformal blocks as finite sums of spinning bosonic blocks.

Key words: conformal blocks; crossing equations; Calogero-Sutherland models.

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