Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory

TL;DR

This paper derives character formulae and partition functions for conformal group representations in higher dimensions, generalizing previous results and revealing dimension-dependent splitting in free representations.

Contribution

It introduces new product formulae for conformal group representations in higher dimensions, extending prior work and analyzing dimension-specific behaviors.

Findings

Product formulae for conformal group representations derived

Generalizations of Flato and Fronsdal's results for SO(3,2)

Dimension-dependent splitting in even-dimensional free representations

Abstract

A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations are found. These include generalisations of those found by Flato and Fronsdal for SO(3,2). In even dimensions the products for free representations split into two types depending on whether the dimension is divisible by four or not.