On the Spectrum of Pure Higher Spin Gravity

Abstract

We study the spectrum of pure massless higher spin theories in $Ad{S}_3$. The light spectrum is given by a tower of massless particles of spin $s=2,\cdots ,N$ and their multi-particles states. Their contribution to the torus partition function organises into the vacuum character of the ${\mathcal{W}}_N$ algebra. Modular invariance puts constraints on the heavy spectrum of the theory, and in particular leads to negative norm states, which would be inconsistent with unitarity. This negativity can be cured by including additional light states, below the black hole threshold but whose mass grows with the central charge. We show that these states can be interpreted as conical defects with deficit angle $2\pi (1-1/M)$. Unitarity allows the inclusion of such defects into the path integral provided $M\ge N$.

arXiv comment33 pages, v2: references added, v3: minor typos corrected, published version

References in corpus (17)

• Quantum Gravity Partition Functions in Three Dimensions
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• One-loop Partition Functions of 3D Gravity
• Higher Spin Black Holes
• Bounding the Space of Holographic CFTs with Chaos
• Averaging Over Narain Moduli Space
• A theory of reparameterizations for AdS${}_3$ gravity
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Higher spin AdS_3 supergravity and its dual CFT
• What is the gravity dual of a chiral primary?
• Quantum W-symmetry in AdS_3
• The Heat Kernel on AdS_3 and its Applications
• Lightcone Modular Bootstrap and Pure Gravity
• Rademacher Expansions and the Spectrum of 2d CFT
• Constraints on Higher Spin CFT${}_2$
• Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap

Cited by in corpus (12)

• Bootstrapping Non-Invertible Symmetries
• Harmonic analysis of 2d CFT partition functions
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Wormholes and Spectral Statistics in the Narain Ensemble
• Narain to Narnia
• Comments on the holographic description of Narain theories
• AdS${}_3$ Gravity and RCFT Ensembles with Multiple Invariants
• Higher spin AdS${}_3$ gravity and Tits-Satake diagrams
• Higher-spin gauge theories in three spacetime dimensions
• Finiteness of 3D higher spin gravity Landscape
• The Schwarzian sector of higher spin CFTs
• Higher spin wormholes from modular bootstrap