Higher Spin Gravities and Deformation Quantization
Abstract:
We present a complete solution to the problem of Formal Higher Spin
Gravities --- formally consistent field equations that gauge a given
higher spin algebra and describe free higher spin fields upon
linearization. The problem is shown to be equivalent to constructing
a certain deformation of the higher spin algebra as an associative
algebra. Given this deformation, all interaction vertices are
explicitly constructed. All formal solutions of the equations are
explicitly described in terms of an auxiliary Lax pair, the
deformation parameter playing the role of the spectral one. We also
discuss a natural set of observables associated to such theories,
including the holographic correlation functions. There is an
interesting extension of the Deformation Qunatization inspired by
this construction.