Intertwining Operator Realization of the AdSCFT Correspondence.pdf

Intertwining Operator Realization of the AdS/CFT Correspondence V.K. Dobrev∗ Arnold Sommerfeld Institute for Mathematical Physics Technical University Clausthal Leibnizstr. 10, 38678 Clausthal-Zellerfeld, Germany 9 asvd@rz.tu-clausthal.de 9 9 1 Abstract r p A We give a group-theoretic interpretation of the AdS/CFT correspondence as relation of representation equivalence between representations of the confor- 0 3 mal group describing the bulk AdS fields φ, their boundary fields φ0 and the coupled to the latter boundary conformal operators O. We use two kinds 2 of equivalences. The first kind is equivalence between the representations de- v 4 scribing the bulk fields and the boundary fields and it is established here. The 9 second kind is the equivalence between conjugated conformal representations 1 related by Weyl reflection, e.g., the coupled fields φ0 and O. Operators 2 1 realizing the first kind of equivalence for special cases were actually given by 8 Witten and others - here they are constructed in a more general setting from 9 the requirement that they are intertwining operators. The intertwining oper- / h ators realizing the second kind of equivalence are provided by the standard t - conformal two-point functions. Using both equivalences we find that the bulk p field has in fact two boundary fields, namely, the c