Note on the boundary terms in AdS/CFT correspondence for Rarita-Schwinger field

TL;DR

This paper analyzes the boundary terms necessary for the Rarita-Schwinger field in AdS/CFT, showing how to fix these terms to ensure correct correlation functions in the boundary CFT.

Contribution

It determines the boundary terms for massless and massive Rarita-Schwinger fields in AdS/CFT, ensuring proper variational principle and correlation functions.

Findings

Boundary term fixes the variational principle for Rarita-Schwinger fields.

Reproduces known two-point correlation functions in boundary CFT.

Clarifies boundary conditions for massless and massive cases.

Abstract

In this letter the boundary problem for massless and massive Rarita-Schwinger field in the AdS/CFT correspondence is considered. The considerations are along the lines of a paper by Henneaux (hep-th/9902137) and are based on the requirement the solutions to be a stationary point for the action functional. It is shown that this requirement, along with a definite asymptotic behavior of the solutions, fixes the boundary term that must be added to the initial Rarita-Schwinger action. It is also shown that the boundary term reproduce the known two point correlation functions of certain local operators in CFT living on the boundary.