Conformal Correlation functions in four dimensions from Quaternionic Lauricella system

TL;DR

This paper develops a quaternionic Lauricella system to express four-dimensional conformal correlation functions, generalizing the two-dimensional case and providing a new mathematical framework for conformal field theories.

Contribution

It introduces a quaternionic Lauricella system to represent four-dimensional conformal correlation functions, extending the two-dimensional Lauricella framework to higher dimensions.

Findings

Representation of 4D conformal correlation functions using quaternionic Lauricella system

Generalization of 2D Lauricella solutions to 4D conformal groups

Mathematical framework connecting quaternions and conformal field theory

Abstract

Correlation functions in Euclidean conformal field theories in four dimensions are expressed as representations of the conformal group $SL(2,\H)$, $\H$ being the field of quaternions, on the configuration space of points. The representations are obtained in terms of Lauricella system for quaternions. It generalizes the two-dimensional case, wherein the $N$-point correlation function is expressed in terms of solutions of Lauricella system on the configuration space of $N$ points on the complex plane, furnishing representation of the conformal group $SL(2,\C)$.