We study conical defect geometries in the SL(N ) Chern-Simons formulation of higher spin gauge theories in AdS 3 . We argue that (for N ≥ 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 AdS 3 spacetimes. Remarkably, the spectrum of smooth SL(N, C) solutions, after an appropriate analytic continuation, exactly matches that of the so-called "light primaries" in the minimal model W N CFTs at finite N . This gives a candidate bulk interpretation of the latter states in the holographic duality proposed in [1].1 See [2] for a review and a comprehensive list of references.

We propose a refinement of the Gaberdiel-Gopakumar duality conjecture between W N conformal field theories and 2+1-dimensional higher spin gravity. We make an identification of generic representations of the W N CFT in the semiclassical limit with bulk configurations. By studying the spectrum of the semiclassical limit of the W N theories and mapping to solutions of Euclidean Vasiliev gravity at λ = −N , we propose that the 'light states' of the W N minimal models in the 't Hooft limit map not to the conical defects of the Vasiliev theory, but rather to bound states of perturbative scalar fields with these defects. Evidence for this identification comes from comparing charges and from holographic relations between CFT null states and bulk symmetries. We also make progress in understanding the coupling of scalar matter to sl(N ) gauge fields.

Abstract:We revisit the construction of multi-centered solutions in three-dimensional anti-de Sitter gravity in the light of the recently discovered connection between particle worldlines and classical Virasoro conformal blocks. We focus on multi-centered solutions which represent the backreaction of point masses moving on helical geodesics in global AdS 3 , and argue that their construction reduces to a problem in Liouville theory on the disk with Zamolodchikov-Zamolodchikov boundary condition. In order to construct the solution one needs to solve a certain monodromy problem which we argue is solved by a vacuum classical conformal block on the sphere in a particular channel. In this way we construct multi-centered gravity solutions by using conformal blocks special functions. We show that our solutions represent left-right asymmetric configurations of operator insertions in the dual CFT. We also provide a check of our arguments in an example and comment on other types of solutions.

We compute the tachyon potential to level 4 in NS superstring field theory. We obtain 89% of the conjectured vacuum energy.

We discuss the quantization and holographic aspects of a class of conical spaces in 2+1 dimensional pure AdS gravity. These appear as topological solitons in the Chern-Simons formulation of the theory and are closely related to the recently studied conical solutions in higher spin gravity. We discuss the classical fluctuations around these solutions, which form exceptional coadjoint orbits of the asymptotic Virasoro group. We argue that the quantization of these solutions leads to nonunitary representations of the Virasoro algebra, on account of their having boundary graviton fluctuations which lower the energy. We propose a framework to quantize them in a semiclassical expansion in the inverse central charge, which we use to compute their one-loop corrected energies. Interestingly, the resulting Virasoro representations contain a null vector, thus providing an appearance of Kac's degenerate representations, which are nonunitary at large central charge, in the context of gravity. We match the computed quantum corrections in the bulk with the properties of a class of primaries in Kac's classification.