External leg amputation in conformal invariant three-point function

TL;DR

This paper explicitly performs external leg amputation in a conformal three-point function involving spinors and a vector, deriving a new star-triangle relation and confirming theoretical expectations about conformal partners.

Contribution

It introduces a new star-triangle relation involving spinors and a vector, and demonstrates the amputation process in conformal invariant functions.

Findings

Amputation replaces a field with its conformal partner.

Derived a new star-triangle relation for spinors and vectors.

Results confirm theoretical predictions about conformal invariance.

Abstract

Amputation of external legs is carried out explicitly for the conformal invariant three-point function involving two spinors and one vector field. Our results are consistent with the general result that amputing an external leg in a conformal invariant Green function replaces a field by its conformal partner in the Green function. A new star-triangle relation, involving two spinors and one vector field, is derived and used for the calculation.