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More on Torus Wormholes in 3d Gravity

Cynthia Yan

TL;DR

This work strengthens the link between semiclassical AdS$_3$ gravity and formal CFT$_2$ ensembles by showing that torus wormholes with insertions yield non-decaying contributions to products of torus correlators at late times. It further analyzes $oldsymbol{ ext{Z}_2}$ quotients of torus wormholes to obtain single-boundary geometries and demonstrates how RT and time-reversal symmetries map to GOE and GSE statistics on the boundary, effectively doubling the torus wormhole partition function. The results connect bulk nonperturbative wormhole effects to boundary ensemble expectations, advancing understanding of spectral statistics in holographic ensembles. Overall, the paper reveals a robust interplay between bulk quotient geometries, boundary OPE data, and random matrix theory classifications in 3d gravity.

Abstract

We study further the duality between semiclassical AdS3 and formal CFT2 ensembles. First, we study torus wormholes (Maldacena-Maoz wormholes with two torus boundaries) with one insertion or two insertions on each boundary and find that they give non-decaying contribution to the product of two torus one-point or two-point functions at late-time. Second, we study the Z2 quotients of a torus wormhole such that the outcome has one boundary. We identify quotients that give non-decaying contributions to the torus two-point function at late-time. We comment on reflection (R) or time-reversal (T) symmetry v.s. the combination RT that is a symmetry of any relativistic field theory. RT symmetry itself implies that to the extent that a relativistic quantum field theory exhibits random matrix statistics it should be of the GOE type. We discuss related implications of these symmetries for wormholes.

More on Torus Wormholes in 3d Gravity

TL;DR

This work strengthens the link between semiclassical AdS gravity and formal CFT ensembles by showing that torus wormholes with insertions yield non-decaying contributions to products of torus correlators at late times. It further analyzes quotients of torus wormholes to obtain single-boundary geometries and demonstrates how RT and time-reversal symmetries map to GOE and GSE statistics on the boundary, effectively doubling the torus wormhole partition function. The results connect bulk nonperturbative wormhole effects to boundary ensemble expectations, advancing understanding of spectral statistics in holographic ensembles. Overall, the paper reveals a robust interplay between bulk quotient geometries, boundary OPE data, and random matrix theory classifications in 3d gravity.

Abstract

We study further the duality between semiclassical AdS3 and formal CFT2 ensembles. First, we study torus wormholes (Maldacena-Maoz wormholes with two torus boundaries) with one insertion or two insertions on each boundary and find that they give non-decaying contribution to the product of two torus one-point or two-point functions at late-time. Second, we study the Z2 quotients of a torus wormhole such that the outcome has one boundary. We identify quotients that give non-decaying contributions to the torus two-point function at late-time. We comment on reflection (R) or time-reversal (T) symmetry v.s. the combination RT that is a symmetry of any relativistic field theory. RT symmetry itself implies that to the extent that a relativistic quantum field theory exhibits random matrix statistics it should be of the GOE type. We discuss related implications of these symmetries for wormholes.
Paper Structure (20 sections, 143 equations, 14 figures, 1 table)

This paper contains 20 sections, 143 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Torus one-point function wormhole
  3. $\Delta\rightarrow0$ limit
  4. Lorentzian torus limit
  5. Torus two-point function wormholes
  6. Large time-separation limit
  7. Single-boundary quotients of a torus wormhole
  8. Semi-classical gravity calculation
  9. CFT calculation
  10. Comments on RT symmetry
  11. JT gravity
  12. Introduction
  13. Product of two one-point functions
  14. Product of two two-point functions
  15. crosscap
  16. ...and 5 more sections

Figures (14)

  • Figure 1: (a) Analogy between a 3d solid torus and a 2d disk (b) Analogy between a 3d torus wormhole and a 2d cylinder
  • Figure 2: (a) $\mathbb{Z}_2$ quotient of a cylinder in 2d (b) $\mathbb{Z}_2$ quotients of a torus wormhole in 3d
  • Figure 3: A Maldacena-Maoz wormhole with two boundaries both Riemann spheres with three light insertions
  • Figure 4: A torus represented as a square with sides identified.
  • Figure 5: (a) $\mathbb{Z}_2$ quotient of a cylinder in 2d (b) $\mathbb{Z}_2$ quotients of a torus wormhole in 3d
  • ...and 9 more figures