Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D

Abstract It was recently shown that multi-point 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 reduce...

Full description

Saved in:
Bibliographic Details
Main Authors: Ilija Burić, Sylvain Lacroix, Jeremy Mann, Lorenzo Quintavalle, Volker Schomerus
Format: article
Language:EN
Published: SpringerOpen 2021
Subjects:
Online Access:https://doaj.org/article/a4a8ab1a4b5245bba0eb72703e7066b9
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Abstract It was recently shown that multi-point 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 3-point tensor structures for all vertices of 3- and 4-dimensional 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 Calogero-Moser-Sutherland 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 mixed-symmetry tensor fields. The results thereby also apply to comb channel vertices of 5- and 6-point functions in arbitrary dimension.