Constraining conformal field theories with a higher spin symmetry

Details Constraining conformal field theories with a higher spin symmetry Constraining conformal field theories with a higher spin symmetry

2011-12-05

arxiv.org/abs/1112.1016v1

Physics

High Energy Physics

High Energy Physics - Theory

61 pages, 1 figure

Scientific paper

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.

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