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Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory
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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.
Forward citations
Cited by 3 Pith papers
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From chiral to conformal anomalies: a double copy perspective for CFT correlators
Squaring the chiral-anomaly three-current correlator, in its five-dimensional flat-space limit, reproduces the conformal-anomaly contribution to the stress-tensor three-point function.
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Symmetric formulation for higher spin correlators, quantum effective action and anomaly
The trace anomaly of the higher-spin conformal effective action is shown to be the single source of both trace and gauge anomalies, with a 2s-derivative structure in d=4.
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Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins
For equal-spin currents up to spin four, conserved three-point correlators can be constructed explicitly as linear combinations of products of spin-one and spin-two Osborn-Petkou building blocks.
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