期刊
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
卷 28, 期 31, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217751X13501625
关键词
Conformal field theory; gauge algebra; higher-spin gravity
资金
- ARC [AUWB-2010-10/15-UMONS-1]
- Alexander von Humboldt Foundation
- RFBR grant [11-02-00814, 1202-31837]
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 listed out, we obtain that the Eastwood-Vasiliev algebra is the unique solution for d = 4 and d >= 7. 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(d), 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.
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