Boundary terms in the AdS/CFT correspondence for spinor fields

TL;DR

This paper determines the specific boundary term needed in the Dirac action within the AdS/CFT framework to ensure a well-defined variational principle for spinor fields in anti-de Sitter space.

Contribution

It identifies the precise boundary term and coefficient required for the Dirac action in AdS/CFT, ensuring stationarity of solutions.

Findings

The boundary term fixes the action's stationarity for Dirac solutions.

The coefficient of the boundary term is explicitly determined.

Ensures consistency of spinor field boundary conditions in AdS/CFT.

Abstract

The requirement that the action be stationary for solutions of the Dirac equations in anti-de Sitter space with a definite asymptotic behaviour is shown to fix the boundary term (with its coefficient) that must be added to the standard Dirac action in the AdS/CFT correspondence for spinor fields.