Wormholes in finite cutoff JT gravity: A study of baby universes and (Krylov) complexity

TL;DR

This work analyzes finite-cutoff JT gravity deformed by a $T\bar{T}$ operator, applying the Complexity = Volume proposal to study late-time interior growth. It constructs the deformed boundary Schwarzian dynamics via a kernel, yielding a deformed propagator and bulk partition functions that modify the spectrum through $E(\lambda)=\frac{1}{4\lambda}(1-\sqrt{1-8\lambda E})$, and it computes disk, trumpet, and double-trumpet amplitudes along with correlation functions. The study further computes the Hartle-Hawking wavefunction and baby-universe emission probabilities in the deformed theory, linking these to the ramp of the spectral form factor and to nonperturbative changes in the moduli-space volume via the spectral curve. A key finding is that the ERB length saturates faster under the $T\bar{T}$ deformation (for $\lambda<0$), accompanied by enhanced baby-universe emission, and a preserved but modified connection to Krylov complexity, suggesting a robust interplay between quantum chaos, holographic interior growth, and matrix-model dynamics in deformed JT gravity.

Abstract

In this paper, as an application of the `Complexity = Volume' proposal, we calculate the growth of the interior of a black hole at late times for finite cutoff JT gravity. Due to this integrable, irrelevant deformation, the spectral properties are modified non-trivially. The Einstein-Rosen Bridge (ERB) length saturates faster than pure JT gravity. We comment on the possible connection between Krylov Complexity and ERB length for deformed theory. Apart from this, we calculate the emission probability of baby universes for the deformed theory and make remarks on its implications for the ramp of the Spectral Form Factor. Finally, we compute the correction to the volume of the moduli space due to the non-perturbative change of the spectral curve because of the finite cutoff at the boundary.

Figures (6)

• Figure 1: Figure describing the Euclidean and Lorentzian parts of emission of the baby universe.
• Figure 2: The growth of ERB length and the emission of baby universes are shown in the figure.
• Figure 3: Effective matrix potential for deformed JT gravity with a saddle point at $\frac{1}{4\lambda}$ marked by the dashed line
• Figure 4: The growth and saturation of ERB length for $T\bar{T}$ deformed theory.
• Figure 5: Plots showing the growth of the ERB for JT gravity and $T\bar{T}$ deformed JT gravity