Supersymmetric Higher-Spin Gauge Theories in any $d$ and their Coupling Constants within BRST Formalism

Abstract

Nonlinear field equations for the supersymmetric higher-spin gauge theory describing totally symmetric bosonic and fermionic massless fields along with hook-type bosonic fields of all spins in any space-time dimension are presented. One of the novel features of the proposed formalism is that the $osp(1,2)$ invariance and factorisation conditions are formulated within the BRST formalism, that greatly simplifies the form of nonlinear HS equations. To match the list of vertices found by Metsaev, higher-spin gauge theory is anticipated to possess an infinite number of independent coupling constants. A conjecture that these coupling constants result from the locality restrictions on the elements of the factorisation ideal is put forward.

46 pages, The paper was prepared for publication in "Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser" but then was resubmitted to JHEP due to some nonscientific issues raised by JPA, V2 minor corrections: typos and sign factors fixed, acknowledgements and reference added, V3 clarifications and acknowledgement added, matches the published version