Constraining conformal field theories with a higher spin symmetry

Abstract

We study the constraints imposed by the existence of a single higher spin conserved current on a three dimensional conformal field theory. A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of N free bosons or free fermions. This is an extension of the Coleman-Mandula theorem to CFT's, which do not have a conventional S matrix. We also briefly discuss the case where the higher spin symmetries are "slightly" broken.

61 pages, 1 figure

References in corpus (4)

• Chern-Simons Theory with Vector Fermion Matter
• Conformal Partial Waves: Further Mathematical Results
• Vector Models in the Singlet Sector at Finite Temperature
• Higher Spin Realization of the dS/CFT Correspondence

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