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

By Nicolas Boulanger, Dmitry Ponomarev, E. D. Skvortsov, M. Taronna. 2013

139 citations recorded by the source corpus.

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 > 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 AdSd, 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.

Subfields: Algebra and Number Theory, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7d5f28aadec00a13f56dc94ee7a22cf3943a69ae

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Citations in the corpus

Light-front higher-spin theories in flat space (2016, background): “This is certainly not true in higher-spin theories where the spectrum should contain infinitely many massless particles [25, 44, 47, 48].”
Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, background): “This spectacular property was expected since the formulation of the higher-spin interaction problem [27] and comes from the structure of the higher-spin algebra, which is to large extent unique [28, 29].”
Causality constraints in conformal field theory (2015, methodology): “This is a part of the Maldacena-Zhiboedov theorem in d = 3 [45] and has been demonstrated in higher dimensions using properties of higher spin algebras [46].”
Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT (2014, unknown): “The question of consistency of an interacting AdS5 theory involving mixed-symmetry fields goes beyond the cubic order and requires, in particular, the closure of the symmetry algebra [89].”