We present gauge invariant, self adjoint Einstein operators for mixed symmetry higher spin theories. The result applies to multi-forms, multi-symmetric forms and mixed antisymmetric and symmetric multiforms, generalizing previous results for combinations of these cases. It also yields explicit action principles for these theories in terms of their minimal covariant field content. For known cases, these actions imply the mixed symmetry equations of motion of Labastida. The result is based on a calculus for handling normal ordered operator expressions built from quantum generators of the underlying constraint algebras.

We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Our models mimic Dirac-Born-Infeld theory but it is unclear whether they are Lagrangian.Comment: 9 pages LaTe

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N = 2 supergravities. By virtue of the cmap, these spinning particles move in quaternionic Kähler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generating special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston's complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kähler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.

We present the Becchi–Rouet–Stora–Tyutin (BRST) cohomologies of a class of constraint (super) Lie algebras as detour complexes. By interpreting the components of detour complexes as gauge invariances, Bianchi identities, and equations of motion, we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric, and Kähler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form Kähler electromagnetism. We also discuss how our results generalize to other special geometries.

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