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

In a recent paper Klebanov and Witten [I. Klebanov, E. Witten, AdS/CFT Correspondence and Symmetry Breaking, 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 Greenʹs 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.