Conformal symmetry in non-local field theories

TL;DR

This paper demonstrates that a specific class of non-local free field theories exhibits conformal symmetry across all dimensions, and explores their symmetry properties and operator product expansions.

Contribution

It identifies conformal symmetry in non-local free field theories and derives associated Noether currents, Ward identities, and operator product expansions.

Findings

Conformal symmetry holds in the studied non-local theories across dimensions.

Explicit forms of Noether currents and Ward identities are derived.

Operator product expansion with the energy-momentum tensor is analyzed.

Abstract

We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the translation, rotation and scale symmetries. The operator product expansion of the energy-momentum tensor with quasi-primary fields is also investigated.