Fermions in Geodesic Witten Diagrams

TL;DR

This paper develops an embedding formalism for fermions in AdS and demonstrates how geodesic Witten diagrams with fermion exchange relate to conformal partial waves, simplifying calculations in AdS/CFT correspondence.

Contribution

It introduces a formalism for fermionic fields in AdS and shows how to decompose Witten diagrams with fermion exchange using geodesic representations.

Findings

Fermion exchange GWD is equivalent to spin-1/2 conformal partial waves.

Explicit decomposition of fermionic Witten diagrams using split representation.

Geodesic representation provides an efficient basis for computations.

Abstract

We develop the embedding formalism for odd dimensional Dirac spinors in AdS and apply it to the (geodesic) Witten diagrams including fermionic degrees of freedom. We first show that the geodesic Witten diagram (GWD) with fermion exchange is equivalent to the conformal partial waves associated with the spin one-half primary field. Then, we explicitly demonstrate the GWD decomposition of the Witten diagram including the fermion exchange with the aid of the split representation. The geodesic representation of CPW indeed gives the useful basis for computing the Witten diagrams.