A Fedosov-quantized Wigner function and the Feigin-Felder-Shoikhet trace yield a manifestly covariant action for scalar matter coupled to conformal higher-spin backgrounds.
Type-B Formal Higher Spin Gravity
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abstract
We propose non-linear equations for the formal Type-B Higher Spin Gravity that is dual to the free fermion or to the Gross-Neveu model, depending on the boundary conditions. The equations are directly obtained from the first principles: the gauge invariance of the CFT partition function on an arbitrary background for single-trace operators. We also get equations describing propagation of certain mixed-symmetry fields over higher spin flat backgrounds.
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Scalar Field on a higher-spin Background via Fedosov quantization
A Fedosov-quantized Wigner function and the Feigin-Felder-Shoikhet trace yield a manifestly covariant action for scalar matter coupled to conformal higher-spin backgrounds.