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.