Higher Spin Double Field Theory : A Proposal

We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to $\mathbf{O}(4,4)$ T-duality, doubled diffeomorphisms, $\mathbf{Spin}(1,3)$ local Lorentz symmetry and, separately, $\mathbf{HS}(4)$ higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.