Abstract
In this work we investigate the matrix elements of the energy-momentum tensor for massless on-shell states in four-dimensional unitary, local, and Poincar\'e covariant quantum field theories. We demonstrate that these matrix elements can be parametrised in terms of covariant multipoles of the Lorentz generators, and that this gives rise to a form factor decomposition in which the helicity dependence of the states is factorised. Using this decomposition we go on to explore some of the consequences for conformal field theories, deriving the explicit analytic conditions imposed by conformal symmetry, and using examples to illustrate that they uniquely fix the form of the matrix elements. We also provide new insights into the constraints imposed by the existence of massless particles, showing in particular that massless free theories are necessarily conformal.
Highlights
As with any quantum field theories (QFTs), the correlation functions in conformal field theories (CFTs) completely encode the dynamics of these theories
A characteristic property of CFTs is that the conformal symmetry significantly constrains the form of the correlation functions, reducing the classification of these objects to the determination of a series of constant parameters
Most studies of the CFT three-point functions involving the energymomentum tensor (EMT) have focused on cases where the other fields have lower values of absolute helicity jhj, since increasing jhj quickly leads to complicated expressions
Summary
As with any quantum field theories (QFTs), the correlation functions in conformal field theories (CFTs) completely encode the dynamics of these theories. Most studies of the CFT three-point functions involving the EMT have focused on cases where the other fields have lower values of absolute helicity jhj, since increasing jhj quickly leads to complicated expressions Because these three-point functions are directly related to the massless onshell EMT matrix elements, via a projection of the Lorentz components of the fields, it turns out that this increase in complexity is a different realization of the fact that the number of independent covariant structures in the form factor expansion increases with jhj.
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