From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models

Schomerus, Volker; Sobko, Evgeny

Preprint/Report

PUBDB-2017-11881

From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models

Schomerus, V. (Corresponding author)DESY* ; Sobko, E.DESY*

2017

[10.3204/PUBDB-2017-11881]

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Please use a persistent id in citations: doi:10.3204/PUBDB-2017-11881

Report No.: DESY-17-177; NORDITA-2017-105; arXiv:1711.02022

Abstract: In 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. To this end, the analysis of [1] is extended to arbitrary dimensions and to the case of boundary two-point functions. In particular, we construct the potential for any set of external tensor fields. Some of the resulting Schrödinger equations are mapped explicitly to the known Casimir equations for 4-dimensional seed conformal blocks. Our approach furnishes solutions of Casimir equations for external fields of arbitrary spin and dimension in terms of functions on the conformal group. This allows us to reinterpret standard operations on conformal blocks in terms of group-theoretic objects. In particular, we shall discuss the relation between the construction of spinning blocks in any dimension through differential operators acting on seed blocks and the action of left/right invariant vector fields on the conformal group.

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