Spinning States and Unitarity in 3D Gravity

TL;DR

This paper explores how adding spinning states in 3D gravity can cancel negative densities of states, interpret these states as bulk defects or overspinning geometries, and analyze their properties and correlators.

Contribution

It demonstrates that certain spinning states can resolve spectral negativities and identifies overspinning geometries with smooth pure gravity solutions, expanding understanding of 3D gravity spectra.

Findings

Spinning states below the black hole threshold cancel negativities.

Overspinning BTZ geometries can cure spectral negativities while maintaining the gap.

Overspinning geometries exhibit causal pathologies and contain quasinormal modes.

Abstract

We revisit the proposal to cure the negative density of states in the three-dimensional gravitational path integral by adding spinning states whose spin scales with the central charge. We show that sub-extremal and extremal spinning states below the black hole threshold can cancel the known negativities, and interpret these states as bulk spinning defects. Additionally, certain overspinning states above the black hole threshold can cure these negativities while preserving the spectral gap. Previously interpreted as classical spinning strings, we instead identify these overspinning states with overspinning BTZ geometries, which are smooth pure gravity quotients of AdS$_3$ with no fixed points. All of these spinning geometries exhibit causal pathologies in their Lorentzian continuations. Moreover, the overspinning geometries arise from mixed elliptic-hyperbolic identifications and contain a right-moving temperature and quasinormal modes. We also generalize the computation of scalar correlators to the extremal and overspinning backgrounds.