Conformal correlation functions in four dimensions from quaternionic Lauricella system

摘要

Correlation functions in four-dimensional Euclidean conformal field theories are expressed in terms of representations of the conformal groupSL(2,H),Hbeing the field of quaternions, on the configuration space of points. The representations are obtained in terms of a Lauricella system derived using quaternions. It generalizes the two-dimensional case, wherein theN-point correlation function is expressed in terms of solutions of Lauricella system on the configuration space ofNpoints on the complex plane, furnishing representation of the conformal groupSL(2,C).