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 Corr espondence and Symmetry Breaking, hep-th/9905104] proposed to formulate the AdS/CFT correspondence principle by taking an "irregular boundary conditio n" 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 cho ice 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 c onsiderations are valid to all orders in perturbation theory. (C) 1999 Publ ished by Elsevier Science B.V. All rights reserved.