Regular and irregular boundary conditions in AdS/CFT correspondence for spinor field

TL;DR

This paper extends the AdS/CFT correspondence framework to include irregular boundary conditions for interacting spinor fields, deriving modified Green's functions and proving their validity in perturbation theory.

Contribution

It generalizes the irregular boundary condition approach from scalar to spinor fields with interactions, introducing a Legendre transform relation for the action.

Findings

Derived the modified Green's function for spinor fields with irregular boundary conditions.

Proved the validity of the approach to all orders in perturbation theory.

Established the relation between the new and usual actions via Legendre transform.

Abstract

In a recent paper Klebanov and Witten (hep-th/9905104) proposed to formulate the AdS/CFT correspondence principle by taking an "irregular boundary condition" for a scalar field. In this paper we generalize this idea to the case of spinor field with interaction. The action functional following from the choice of irregular boundary conditions and which must be used in the AdS/CFT correspondence is related to the usual action by a Legendre transform. For the new theory we found the modified Green's function that must be used for internal lines in calculating higher order graphs. It is proved that the considerations are valid to all orders in perturbation theory.