Higher-spin self-dual gravity arises by embedding 4D spacetime into an infinite-dimensional manifold of holomorphic planes in a boundedly deformed twistor space, with higher-spin symmetries from different embeddings and integrability via a Lax pair.
Analysis of Higher Spin Field Equations in Four Dimensions
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abstract
The minimal bosonic higher spin gauge theory in four dimensions contains massless particles of spin s=0,2,4,.. that arise in the symmetric product of two spin 0 singletons. It is based on an infinite dimensional extension of the AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the gravitational gauge fields are treated exactly and the gravitational curvatures and the higher spin gauge fields as weak perturbations. We also give the details of an explicit iteration procedure for obtaining the field equations to arbitrary order in curvatures. In particular, we highlight the structure of all the quadratic terms in the field equations.
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Higher-spin self-dual gravity from holomorphic planes in twistor space
Higher-spin self-dual gravity arises by embedding 4D spacetime into an infinite-dimensional manifold of holomorphic planes in a boundedly deformed twistor space, with higher-spin symmetries from different embeddings and integrability via a Lax pair.