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On Complexity of Jackiw-Teitelboim Gravity

Mohsen Alishahiha

TL;DR

This work analyzes holographic complexity in Jackiw-Teitelboim gravity using the complexity=action proposal. By implementing a UV regularization that induces a behind-horizon cutoff (à la Akhavan), the authors compute the on-shell Wheeler-DeWitt action for an AdS$_2$ black hole with a linear dilaton and show that the complexity grows linearly at late times, in contrast to earlier constant-velocity results. The analysis is extended to a general 2D dilaton gravity, where fluctuations about a constant dilaton reduce to JT dynamics and a topological boundary term crucially contributes to the complexity, yielding near-extremal growth rates that match expectations from charged higher-dimensional reductions. For a concrete potential derived from dimensional reduction of 4D Maxwell-Einstein gravity, the late-time rate takes the form $\frac{dI}{d\tau}=S_0 T+\frac{\pi \ell}{G} T^2$, illustrating near-extremal behavior and reinforcing the role of boundary terms in CA complexity. Overall, the results highlight sensitivity of CA complexity to regularization and boundary terms and suggest consistency with holographic descriptions of nearly conformal systems such as the SYK model.

Abstract

Using "complexity=action" proposal we compute complexity for Jackiw-Teitelboim gravity assuming that a UV cutoff enforces us to have a cut off behind the horizon. We find that the resultant complexity exhibits the late time linear growth. It is also consistent with the case where the corresponding Jackiw-Teitelboim gravity is obtained by dimensional reduction from higher dimensional gravities. To this work certain counter term on the cut off surface behind horizon is needed.

On Complexity of Jackiw-Teitelboim Gravity

TL;DR

This work analyzes holographic complexity in Jackiw-Teitelboim gravity using the complexity=action proposal. By implementing a UV regularization that induces a behind-horizon cutoff (à la Akhavan), the authors compute the on-shell Wheeler-DeWitt action for an AdS black hole with a linear dilaton and show that the complexity grows linearly at late times, in contrast to earlier constant-velocity results. The analysis is extended to a general 2D dilaton gravity, where fluctuations about a constant dilaton reduce to JT dynamics and a topological boundary term crucially contributes to the complexity, yielding near-extremal growth rates that match expectations from charged higher-dimensional reductions. For a concrete potential derived from dimensional reduction of 4D Maxwell-Einstein gravity, the late-time rate takes the form , illustrating near-extremal behavior and reinforcing the role of boundary terms in CA complexity. Overall, the results highlight sensitivity of CA complexity to regularization and boundary terms and suggest consistency with holographic descriptions of nearly conformal systems such as the SYK model.

Abstract

Using "complexity=action" proposal we compute complexity for Jackiw-Teitelboim gravity assuming that a UV cutoff enforces us to have a cut off behind the horizon. We find that the resultant complexity exhibits the late time linear growth. It is also consistent with the case where the corresponding Jackiw-Teitelboim gravity is obtained by dimensional reduction from higher dimensional gravities. To this work certain counter term on the cut off surface behind horizon is needed.

Paper Structure

This paper contains 4 sections, 34 equations, 1 figure.

Table of Contents

  1. Introduction
  2. CA complexity for Jackiw-Teitelboim gravity
  3. CA complexity for a general 2D gravity
  4. Conclusions

Figures (1)

  • Figure 1: Penrose diagram of AdS$_2$ geometry. The green area is covered by global coordinate while the diamond shown by dashed lines is covered by Rindler coordinates.The WDW patch is shown by blue color. The inside cutoff $r_0$ is given by in terms of UV cutoff by $r_0 r_{\rm Max}^2=r_h^3$ at leading order. This figure is taken from the ref. Akhavan:2018wla.