Spinors and the AdS/CFT correspondence

TL;DR

This paper explores the relationship between free massive spinor fields in Euclidean AdS space and boundary conformal field theories, demonstrating how boundary conditions influence the partition function and correlators.

Contribution

It provides a detailed calculation of the partition function dependence on boundary spinors, linking bulk spinor dynamics to boundary CFT correlators.

Findings

Partition function depends on boundary spinor boundary conditions.

Boundary conditions correspond to a boundary spinor with a projection.

Results match the generating functional of boundary spinor correlators.

Abstract

We consider a free massive spinor field in Euclidean Anti-de Sitter space. The usual Dirac action in bulk is supplemented by a certain boundary term. The boundary conditions of the field are parametrized by a spinor on the boundary, subject to a projection. We calculate the dependence of the partition function on this boundary spinor. The result agrees with the generating functional of the correlation functions of a quasi-primary spinor operator, of a certain scaling dimension, in a free conformal field theory on the boundary.