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Conical defects in higher spin theories. (English) Zbl 1309.83080

Summary: We study conical defect geometries in the \(\operatorname{SL}(N,\mathbb{R}) \times \operatorname{SL}(N,\mathbb{R})\) (and \(\operatorname{SL}(N,\mathbb{C})\)) Chern-Simons formulation of higher spin gauge theories in \(\operatorname{AdS}_{3}\). We argue that (for \(N \geq 4\)) there are special values of the deficit angle for which these geometries are actually smooth configurations of the underlying theory. We also exhibit a gauge in which these geometries can be viewed as wormholes interpolating between two distinct asymptotically \(\operatorname{AdS}_{3}\) spacetimes. Remarkably, the spectrum of smooth \(\operatorname{SL}(N,\mathbb{C})\) solutions, after an appropriate analytic continuation, exactly matches that of the so-called “light primaries” in the minimal model \({\mathcal{W}_N}\) CFTs at finite \(N\). This gives a candidate bulk interpretation of the latter states in the holographic duality proposed in [M. R. Gaberdiel et al., Phys. Rev. D 83, No. 6, Article No. 066007, 33 p. (2011), doi:10.1103/PhysRevD.83.066007].

MSC:

83C75 Space-time singularities, cosmic censorship, etc.
81T10 Model quantum field theories
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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