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Surgery and statistics in 3d gravity

Jan de Boer, Joshua Kames-King, Boris Post

Abstract

We extend the correspondence between universal statistical features of large-$c$ 2d CFTs and surgery methods in pure AdS$_3$ quantum gravity. In particular, we introduce a method that we call RMT surgery, which relates a large class of off-shell partition functions in 3d gravity to the spectral statistics of general CFT observables. We apply this method to construct and compute an off-shell Euclidean wormhole whose boundaries are four-punctured spheres, which captures level repulsion in the high-energy sector of the boundary CFT. Using a similar gluing prescription, we also explore a new class of off-shell torus wormholes with trumpet boundaries, contributing to statistical moments of the density of primary states. Lastly, we demonstrate that surgery methods can be used as an intermediate step towards computing Seifert manifolds directly in 3d gravity.

Surgery and statistics in 3d gravity

Abstract

We extend the correspondence between universal statistical features of large- 2d CFTs and surgery methods in pure AdS quantum gravity. In particular, we introduce a method that we call RMT surgery, which relates a large class of off-shell partition functions in 3d gravity to the spectral statistics of general CFT observables. We apply this method to construct and compute an off-shell Euclidean wormhole whose boundaries are four-punctured spheres, which captures level repulsion in the high-energy sector of the boundary CFT. Using a similar gluing prescription, we also explore a new class of off-shell torus wormholes with trumpet boundaries, contributing to statistical moments of the density of primary states. Lastly, we demonstrate that surgery methods can be used as an intermediate step towards computing Seifert manifolds directly in 3d gravity.

Paper Structure

This paper contains 23 sections, 148 equations, 10 figures.

Table of Contents

  1. Introduction
  2. ETH surgery
  3. Non-Gaussianities
  4. RMT surgery
  5. Wormhole partition function
  6. Modular completion
  7. Generalization to other topologies
  8. Trumpets and 3-manifolds
  9. Seifert manifolds from Dehn surgery
  10. Seifert partition function
  11. Matrix model ansatz
  12. Topological recursion
  13. Near-extremal limit
  14. Discussion
  15. Constrained saddles.
  16. ...and 8 more sections

Figures (10)

  • Figure 1: ETH surgery.
  • Figure 2: RMT surgery.
  • Figure 3: Bulk mapping class acting on an annulus$\times S^1$.
  • Figure 4: The ETH and RMT contributions to the variance $\Delta\mathcal{G}^2$ are associated to distinct bulk topologies.
  • Figure 5: RMT surgery in the more general case. The three-valent graph $\Gamma$ is symbolized by a box.
  • ...and 5 more figures