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Abstract

The pp-wave (Penrose limit) in a conformal field theory can be viewed as a special contraction of unitary representations of a conformal group. We study kinematics of conformal fields in the contraction limit by employing a geometric approach where the effect of the contraction can be visualized as an expansion of space-time. We discuss the two common models of space-time as carrier spaces for conformal fields: one is the usual Minkowski space and the other is a coset of the conformal group over its maximal compact subgroup. We show that only the latter manifold and the corresponding conformal representation theory admit a non-singular contraction limit. We also address a question about correlation functions of conformal fields in the pp-wave limit. We argue that finiteness of the (two-point) correlators under contraction can be achieved if their dependence on the coordinates of an R-symmetry group is kept on equal footing with their space-time dependence. This is a manifestation of the fact that in the contraction limit the space-time and R-symmetry groups become indistinguishable. Our results might find applications in actual calculations of correlation functions of composite operators in the ${cal N}=4$ super Yang-Mills theory