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 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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- November 2021
- DOI:
- 10.1007/JHEP11(2021)182
- arXiv:
- arXiv:2108.00023
- Bibcode:
- 2021JHEP...11..182B
- Keywords:
-
- Conformal Field Theory;
- Space-Time Symmetries;
- Differential and Algebraic Geometry;
- Integrable Hierarchies;
- High Energy Physics - Theory;
- Mathematical Physics;
- Mathematics - Quantum Algebra;
- Mathematics - Representation Theory
- E-Print:
- 67 pages, 4 figures, v2: published version, inaccuracies corrected, figure and tables added, two Mathematica notebooks added