Towards N=2 higher-spin supergravity

We review the superfield formulation of N=2 higher-spin supergravity theory in harmonic superspace. The analysis of both the hypermultiplet higher-spin supersymmetries and conformal supersymmetries is performed. The analytic superspace gauging of these symmetries gives rise to a set of unconstrained analytical prepotentials describing N=2 higher-spin off-shell supermultiplets. This procedure naturally yields cubic interaction vertices of N=2 higher spins with the hypermultiplet. Based on these results, the consistent interaction of an infinite tower of N=2 superconformal higher spins with hypermultiplet is presented. Proceeding from this model, a method to construct a consistent interacting theory of N=2 higher-spin supergravity by making use of the conformal compensators is proposed.