Journal
NUCLEAR PHYSICS B
Volume 865, Issue 1, Pages 200-215Publisher
ELSEVIER
DOI: 10.1016/j.nuclphysb.2012.07.027
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Funding
- MIUR-PRIN contract [2009-KHZKRX-005]
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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 suggests 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. (C) 2012 Elsevier B.V. All rights reserved.
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