The Case of the Missing Gates: Complexity of Jackiw-Teitelboim Gravity

TL;DR

The paper probes holographic complexity in the Jackiw-Teitelboim (JT) gravity throat of near-extremal Reissner-Nordström black holes, testing complexity=action (CA) and complexity=volume (CV) conjectures. A naive CA calculation in JT yields zero late-time growth, contradicting the known RN results; the authors show this arises from an inappropriate boundary term introduced during dimensional reduction. By carefully analyzing the dimensional reduction and the role of Maxwell boundary terms, they demonstrate that removing the spurious boundary term restores the expected linear growth of action, aligning JT/CA with RN behavior and highlighting how boundary terms encode ensemble choices. The work thus reveals that holographic complexity is sensitive to internal boundary conditions and that reduced models must preserve correct boundary structures to yield meaningful CA/CV predictions, with implications for SYK-like dynamics and related holographic systems.

Abstract

The Jackiw-Teitelboim (JT) model arises from the dimensional reduction of charged black holes. Motivated by the holographic complexity conjecture, we calculate the late-time rate of change of action of a Wheeler-DeWitt patch in the JT theory. Surprisingly, the rate vanishes. This is puzzling because it contradicts both holographic expectations for the rate of complexification and also action calculations for charged black holes. We trace the discrepancy to an improper treatment of boundary terms when naively doing the dimensional reduction. Once the boundary term is corrected, we find exact agreement with expectations. We comment on the general lessons that this might hold for holographic complexity and beyond.

Figures (5)

• Figure 1: The three regions outside the horizon of a near-extremal RN black hole. The transition from throat to Newtonian region occurs at $r \sim 2r_+$, which is also the approximate location of the top of the potential barrier Brown:2018kvn, and also the approximate location of the curved JT boundary in Fig. \ref{['fig:WDW_patch']}.
• Figure 2: Jackiw-Teitelboim black hole in global AdS$_2$ coordinates. The red curves indicate the outer boundary of the 1+1-dimensional black hole spacetime, while the solid black curves indicate singularities where $\Phi=0$. The dashed diagonal lines show the location of the black hole horizon.
• Figure 3: Jackiw-Teitelboim black hole: Curves of constant Schwarzschild time outside the event horizon are shown in blue.
• Figure 4: Minimal slices for $C=V$ calculation. The left panel shows a 'horizontal' slice with $\nu_L=\nu_R$. On the right, a more general slice with independent values of $\nu_L$, $\nu_R$.
• Figure 5: Wheeler-DeWitt patch for CA calculation.