Quantization of conical spaces in 3D gravity

TL;DR

This paper explores the quantization of conical spaces in 3D AdS gravity, revealing nonunitary Virasoro representations with null vectors and connecting bulk quantum corrections to Kac's degenerate representations.

Contribution

It introduces a semiclassical quantization framework for conical spaces in 3D gravity, linking boundary graviton fluctuations to nonunitary Virasoro representations with null vectors.

Findings

Quantization leads to nonunitary Virasoro representations.

Bulk quantum corrections match properties of Kac's degenerate primaries.

Conical spaces correspond to exceptional coadjoint orbits with null vectors.

Abstract

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.