Conformal Differential Operator in Embedding Space and its Applications

TL;DR

This paper introduces a new differential operator in embedding space to facilitate the construction of conformal blocks, revealing symmetries and relations useful in conformal field theory calculations.

Contribution

It develops a unique differential operator in embedding space and demonstrates its application in constructing conformal blocks with symmetry properties.

Findings

Constructed a unique differential operator for embedding space.

Derived relations satisfied by conformal block components.

Showed invariance under the dihedral group.

Abstract

We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal blocks. We show a number of relations that the components of conformal blocks satisfy and find invariance of our expressions under the dihedral group.