Conformal fields in the pp-wave limit

TL;DR

This paper investigates the behavior of conformal fields under the pp-wave limit, revealing how space-time and R-symmetry merge and identifying the appropriate geometric framework for a non-singular contraction.

Contribution

It demonstrates that only the coset model of conformal space admits a smooth contraction limit and analyzes the correlation functions' behavior in this limit.

Findings

Only the coset space model admits a non-singular contraction.

Correlation functions have a well-defined limit when space-time and R-symmetry dependences merge.

Space-time and R-symmetries become indistinguishable in the pp-wave limit.

Abstract

The pp-wave (Penrose limit) in conformal field theory can be viewed as a special contraction of the unitary representations of the conformal group. We study the kinematics of conformal fields in this limit in 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 the 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 the issue of correlation functions of conformal fields in the pp-wave limit. We show that they have a well-defined contraction limit if their space-time dependence merges with the dependence on the coordinates of the R symmetry group. This is a manifestation of the fact that in the limit the space-time and R symmetries become indistinguishable. Our results might find applications in actual calculations of correlation functions of composite operators in N=4 super Yang-Mills theory.