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Lorentzian Path Integrals and Jackiw-Teitelboim wormholes with imaginary scalars

Jesse Held, Molly Kaplan, Donald Marolf, Zhencheng Wang

TL;DR

This work applies Lorentzian path-integral methods to Jackiw-Teitelboim gravity with an imaginary-valued scalar to study wormholes that connect two AdS boundaries. It constructs constrained Lorentzian wormhole saddles and analyzes their contributions to the connected partition function, finding dominance by the wormhole saddle for imaginary boundary data, in contrast to Euclidean axion wormholes. The analytic continuation reveals a nuanced dependence on the complex boundary parameter $k$, with dominance at purely imaginary $k$ and subdominance in other regimes, aligning with a bulk interpretation in terms of SYK-like physics at complex couplings. The results highlight the sensitivity of wormhole contributions to detailed physical content and suggest further avenues for connecting Lorentzian and Euclidean approaches across wormhole landscapes.

Abstract

The Lorentzian path integral was recently used to argue that standard Euclidean axion wormholes do not dominate computations of connected AdS/CFT partition functions. We now apply similar methods to study the seemingly-analogous Jackiw-Teitelboim wormholes constructed by Garcia-Garcia and Godet using Jackiw-Teitelboim gravity with an imaginary-valued minimally-coupled massless scalar field. However, this time we find that these wormholes do dominate our path integral for the relevant connected partition function. This supports the suggestion by Garcia-Garcia and Godet that contributions from such wormholes parallel the physics of the Sachdev-Ye-Kitaev model at complex couplings. The result also illustrates the sensitivity of wormhole contributions to details of the relevant physics.

Lorentzian Path Integrals and Jackiw-Teitelboim wormholes with imaginary scalars

TL;DR

This work applies Lorentzian path-integral methods to Jackiw-Teitelboim gravity with an imaginary-valued scalar to study wormholes that connect two AdS boundaries. It constructs constrained Lorentzian wormhole saddles and analyzes their contributions to the connected partition function, finding dominance by the wormhole saddle for imaginary boundary data, in contrast to Euclidean axion wormholes. The analytic continuation reveals a nuanced dependence on the complex boundary parameter , with dominance at purely imaginary and subdominance in other regimes, aligning with a bulk interpretation in terms of SYK-like physics at complex couplings. The results highlight the sensitivity of wormhole contributions to detailed physical content and suggest further avenues for connecting Lorentzian and Euclidean approaches across wormhole landscapes.

Abstract

The Lorentzian path integral was recently used to argue that standard Euclidean axion wormholes do not dominate computations of connected AdS/CFT partition functions. We now apply similar methods to study the seemingly-analogous Jackiw-Teitelboim wormholes constructed by Garcia-Garcia and Godet using Jackiw-Teitelboim gravity with an imaginary-valued minimally-coupled massless scalar field. However, this time we find that these wormholes do dominate our path integral for the relevant connected partition function. This supports the suggestion by Garcia-Garcia and Godet that contributions from such wormholes parallel the physics of the Sachdev-Ye-Kitaev model at complex couplings. The result also illustrates the sensitivity of wormhole contributions to details of the relevant physics.
Paper Structure (8 sections, 40 equations, 1 figure)

This paper contains 8 sections, 40 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Partition functions from Lorentzian Path Integrals
  3. Review: Euclidean wormholes in JT gravity
  4. Lorentzian gravitational path integral for wormholes in JT gravity
  5. Wormholes and constrained wormholes
  6. Action and Partition Functions for real boundary conditions
  7. Analytic continuation to general $k\in {\mathbb C}$
  8. Discussion

Figures (1)

  • Figure 1: A sequence of contour plots showing $\Re(iS_{CWH})$ in the complex $\tilde{A}_0$ plane for various $k\in \mathbb C$ and for fixed parameters $\beta=1$, $\phi_b=10^3$. Warmer colors indicate larger $\Re(iS_{CWH})$ while cooler colors indicate smaller values. Green dots mark the saddle $\tilde{A}_0=-\frac{k^2}{\pi \phi_b}$, and the blue and red dashed lines are the steepest descent and ascent contours of the saddle respectively. The solid black line is the integration contour, while the real and imaginary axes are shown using dotted black lines.