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 WN CFT’s: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical WN 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 WN primaries, to all orders in the large central charge expansion.
Highlights
We study the formulation of massless higher-spin gravity on AdS3 in a gauge in which the fundamental variables satisfy free field Poisson brackets
We show that doing so leads to a bulk version of the Coulomb gas formalism for WN CFT’s: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical WN charges
We will refer to the charges Sa as screening charges since, in a sense to be made precise in section 4.4 below, they are a classical limit of the screening charges of the Coulomb gas formalism, see [6]
Summary
We recall the key features of the Chern-Simons formulation of Euclidean higher-spin gauge theories in three-dimensional anti-de-Sitter (AdS) background. We review the boundary conditions that select asymptotically-AdS field configurations, stressing that they can be formulated in many different, albeit equivalent, ways. We focus on boundary conditions belonging to the class of Drinfeld-Sokolov gauges and we confront them with the diagonal gauge that will be analysed
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