Abstract
We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent works. We investigate and detail the structure of the CWIs and their non-perturbative solutions, and compare them to perturbation theory, taking QED and QCD as examples. Exact solutions of CFT’s in the flat background limit in momentum space are matched by the perturbative realizations in free field theories, showing that the origin the conformal anomaly is related to effective scalar interactions, generated by the renormalization of the longitudinal components of the corresponding operators.
Highlights
IntroductionFor instance, which allow to define a program for the bootstrap of higher point functions, as well as other analysis, have so far favoured coordinate space
Correlation functions of 3-point functions play a special role in conformal field theory (CFT) in d = 4 since they can be determined by solving the constraints imposed by the conformal group, which in d = 4 is SO(2, 4)
For instance, which allow to define a program for the bootstrap of higher point functions, as well as other analysis, have so far favoured coordinate space
Summary
For instance, which allow to define a program for the bootstrap of higher point functions, as well as other analysis, have so far favoured coordinate space. Studies of CFT’s based on the standard perturbative expansion in the gauge coupling, such as in N = 4 supersymmetric Yang-Mills theory, as far as the computation of the amplitudes is concerned, have been largely performed in momentum space. A direct solution of the conformal Ward identities - for a given correlation function can be interpreted, in this respect, as being strictly non perturbative, in the sense that it is not related to any coupling but only to the underlying symmetry. Establishing a link between the two approaches in momentum space, with exact CFT solutions on one side and Lagrangian realizations on the other, turns useful for various reasons. A second one is the possibility of offering a simple and physical interpretation of the origin of the conformal anomaly in 3-point functions, for correlators with one or more insertions of stress energy tensors
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