Abstract
We study the formulation of massless higher-spin gravity on AdS3 in a gauge in which the fundamental variables satisfy free field Poisson brackets. This gauge choice leaves a small portion of the gauge freedom unfixed, which should be further quotiented out. We show that doing so leads to a bulk version of the Coulomb gas formalism for W N CFT’s: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical W N charges.
Quantization in these variables can be carried out using standard techniques and makes manifest a remnant of the triality symmetry of W∞[λ]. This symmetry can be used to argue that the theory should be supplemented with additional matter content which is precisely that of the Prokushkin-Vasiliev theory. As a further application, we use our formulation to quantize a class of conical surplus solutions and confirm the conjecture that these are dual to specific degenerate W N primaries, to all orders in the large central charge expansion.
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Campoleoni, A., Fredenhagen, S. & Raeymaekers, J. Quantizing higher-spin gravity in free-field variables. J. High Energ. Phys. 2018, 126 (2018). https://doi.org/10.1007/JHEP02(2018)126
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DOI: https://doi.org/10.1007/JHEP02(2018)126