Quantizing higher-spin gravity in free-field variables

TL;DR

This paper develops a free-field variable formulation of higher-spin gravity in AdS$_3$, revealing a Coulomb gas structure, residual gauge symmetries, and connections to $W_N$ CFTs, with implications for quantization and dualities.

Contribution

It introduces a gauge choice for higher-spin gravity that simplifies quantization and uncovers a Coulomb gas formalism linked to $W_N$ CFTs, highlighting residual symmetries and dualities.

Findings

Residual gauge symmetries correspond to classical screening charges.

Quantization using standard techniques is feasible in this framework.

Conical surplus solutions are confirmed to be dual to degenerate $W_N$ primaries.

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 $W_\infty[\lambda]$. 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.