Quantizing higher-spin gravity in free-field variables

Abstract

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 ∞ [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.

Rectangular W-algebras, extended higher spin gravity and dual coset CFTs

“…With this condition and the residual gauge symmetry, we can put 15) see [12,33,34]. The asymptotic symmetry can be obtained as a classical Hamiltonian reduction of hs M [λ] for the Chern-Simons theory by following the standard procedure in [15][16][17][18].…”

Constraints for three-dimensional higher-spin interactions and conformal correlators

“…There are two other common gauge choices for g " slpN q: the u-gauge which leads to a particularly simple realisation of the W-algebra where the highest non-linearities are quadratic[41], and the diagonal gauge that leads to a free field realisation[42] which therefore can be a good starting point to discuss quantisation[43].…”

Rectangular W algebras and superalgebras and their representations

“…We then compared the results with the spectrum of the coset (1.1) and the mass of conical defect geometry of the higher spin gravity constructed in [16]. In particular, the conformal weights in (3.56) give the information of quantum corrections to the masses of conical defects, and it is an important problem to reproduce them from the gravity theory, see [54,55,56]. It is also desired to have more systematic understanding of degenerate representations including generic M and n.…”

“…55) where h L,K Λ L and hκ m were defined in(3.58) and n is an integer related to the embedding of representations. Moreover, we have introduced h 2N M ω = ω/4 for ω = 0, 2 and h 2N M ω = NM/8 for ω = ±1.…”