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arXiv · 1712.08078

Quantizing higher-spin gravity in free-field variables

Andrea Campoleoni·Stefan Fredenhagen·Joris Raeymaekers
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Abstract

We study the formulation of massless higher-spin gravity on AdS$_3$ 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 $W_\infty[λ]$. 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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Andrea Campoleoni, Stefan Fredenhagen, Joris Raeymaekers. 2018-02-22. Quantizing higher-spin gravity in free-field variables. https://doi.org/10.1007/jhep02(2018)126

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