On holomorphic sector of higher-spin theory

Abstract

Recent investigation of the locality problem for higher-spin fields led to a vertex reconstruction procedure that involved elements of contraction of the original Vasiliev interaction algebra. Inspired by these results we propose the Vasiliev-like generating equations for the holomorphic higher-spin interactions in four dimensions based on the observed contracted algebra. We specify the functional class that admits evolution on the proposed equations and brings in a systematic procedure of extracting all-order holomorphic vertices. A simple consequence of the proposed equations is the space-time locality of the gauge field sector. We also show that vertices come with a remarkable shift symmetry.

Quintic vertices of spin 3, vector and scalar fields

“…Firstly, in our knowledge, quantic vertices did not construct for any models of the theory of higher spin fields. Secondly, in connection with the problem of locality in the high spin theory [8,9,10], examples (7), (17) give local gauge-invariant vertices, which allow to assume the existence of local vertices in higher orders of the perturbation theory.…”

“…Beginning with famous papers of Fradkin and Vasiliev [1,2] and Vasiliev [3,4,5] construction of interactions in the theory of high spin fields [6,7] attracts an increasing interest due to numerous problems arising in this process (for recent discussions see [8,9,10]). At the present, there is strong opinion that the structure of cubic vertices are established very well [11,12,13,14,15,16,17,18,19,20,21] using different methods (deformation procedure in the BV formalism [22,23,24,25], BRST construction [26], light-cone formalism [27]).…”

Supersymmetric quantum chiral higher spin gravity

“…From D = 4 Chiral HiSGRA one can obtain some more consistent models with interacting higher spin fields, both on flat and on anti-de Sitter backgrounds. Namely, it is possible to consider its AdS 4 version and study its application to the AdS 4 /CF T 3 correspondence [15][16][17][18][19]. Another interesting model can be obtained by making a specific kind of dimensional reduction to a three dimensional D = 3 flat space [20,21].…”