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Journal Article

#### On the uniqueness of higher-spin symmetries in AdS and CFT

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##### Fulltext (public)

1305.5180.pdf

(Preprint), 360KB

##### Supplementary Material (public)

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##### Citation

Boulanger, N., Ponomarev, D., Skvortsov, E. D., & Taronna, M. (2013). On the uniqueness
of higher-spin symmetries in AdS and CFT.* International Journal of Modern Physics A,* *28*(31): 1350162. doi:10.1142/S0217751X13501625.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-768E-D

##### Abstract

We study the uniqueness of higher-spin algebras which are at the core of
higher-spin theories in AdS and of CFTs with exact higher-spin symmetry, i.e.
conserved tensors of rank greater than two. The Jacobi identity for the gauge
algebra is the simplest consistency test that appears at the quartic order for
a gauge theory. Similarly, the algebra of charges in a CFT must also obey the
Jacobi identity. These algebras are essentially the same. Solving the Jacobi
identity under some simplifying assumptions spelled out, we obtain that the
Eastwood-Vasiliev algebra is the unique solution for d=4 and d>6. In 5d there
is a one-parameter family of algebras that was known before. In particular, we
show that the introduction of a single higher-spin gauge field/current
automatically requires the infinite tower of higher-spin gauge fields/currents.
The result implies that from all the admissible non-Abelian cubic vertices in
AdS, that have been recently classified for totally symmetric higher-spin gauge
fields, only one vertex can pass the Jacobi consistency test. This cubic vertex
is associated with a gauge deformation that is the germ of the
Eastwood-Vasiliev's higher-spin algebra.