Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory

Abstract

We derive a generating function for all the 3-point functions of higher spin conserved currents in four dimensional conformal field theory. The resulting expressions have a rather surprising factorized form which suggest that they can all be realized by currents built from free massless fields of arbitrary (half-)integer spin s. This property is however not necessarily true also for the higher-point functions. As an illustration we analyze the general 4-point function of conserved abelian U(1) currents of scale dimension equal to three and find that apart from the two free field realizations there is a unique possible function which may correspond to an interacting theory. Although this function passes several non-trivial consistency tests, it remains an open challenging problem whether it can be actually realized in an interacting CFT.

20 pages, LaTeX, references added

References in corpus (4)

• Partial wave expansion and Wightman positivity in conformal field theory
• Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields
• Conformal field theories with infinitely many conservation laws
• Infinite dimensional Lie algebras in 4D conformal quantum field theory

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