Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
Abstract
It was recently shown that multipoint conformal blocks in higher dimensional conformal field theory can be considered as joint eigenfunctions for a system of commuting differential operators. The latter arise as Hamiltonians of a Gaudin integrable system. In this work we address the reduced fourth order differential operators that measure the choice of 3point tensor structures for all vertices of 3 and 4dimensional comb channel conformal blocks. These vertices come associated with a single cross ratio. Remarkably, we identify the vertex operators as Hamiltonians of a crystallographic elliptic CalogeroMoserSutherland model that was discovered originally by Etingof, Felder, Ma and Veselov. Our construction is based on a further development of the embedding space formalism for mixedsymmetry tensor fields. The results thereby also apply to comb channel vertices of 5 and 6point functions in arbitrary dimension.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2108.00023
 Bibcode:
 2021arXiv210800023B
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 67 pages, 3 figures