Four-dimensional conformal field theory using quaternions

TL;DR

This paper develops a four-dimensional quaternionic conformal field theory (QCFT) by extending concepts from two-dimensional complex conformal field theory, exploring its symmetries, operators, and quantization.

Contribution

It introduces a novel quaternionic framework for 4D conformal field theories, expanding the mathematical tools and understanding of higher-dimensional conformal symmetries.

Findings

Constructed quaternionic conformal transformations using quaternion holomorphic functions

Analyzed the stress tensor, conserved charges, and symmetry generators in QCFT

Derived operator product expansions and discussed potential applications

Abstract

We build a four-dimensional quaternion-parametrized conformal field theory (QCFT) using quaternion holomorphic functions as the generators of quaternionic conformal transformations. Taking the two-dimensional complex-parametrized conformal field theory (CCFT) as our model, we study the stress tensor, the conserved charge, the symmetry generators, the quantization conditions and several operator product expansions (OPE's). Future applications also are addressed.