A World without Pythons would be so Simple

TL;DR

The paper establishes a classical-limit converse to the Python's lunch conjecture by showing that bulk operators outside the lunch but inside the outermost extremal surface admit simple boundary reconstruction via HKLL with timefolds, effectively enlarging the causal wedge to the outermost extremal surface. It introduces the simple wedge and its duality to the simple entropy, demonstrates a zigzag/topology-compatible procedure to align the simple, causal, and entanglement wedges, and identifies conditions under which the boundary modular Hamiltonian becomes exactly local. By constructing a coarse-grained state and a corresponding simple state, the work argues for a holographic no-hair-like relation between local modular flow and wedge coincidence, with broader implications for boundary-anchored surfaces, quantum corrections, and complexity censorship in gravity. Overall, the results illuminate how semiclassical bulk dynamics constrain holographic reconstructions and link geometric extremal surfaces to tractable boundary data via controlled coarse-graining and simple operations.

Abstract

We show that bulk operators lying between the outermost extremal surface and the asymptotic boundary admit a simple boundary reconstruction in the classical limit. This is the converse of the Python's lunch conjecture, which proposes that operators with support between the minimal and outermost (quantum) extremal surfaces - e.g. the interior Hawking partners - are highly complex. Our procedure for reconstructing this "simple wedge" is based on the HKLL construction, but uses causal bulk propagation of perturbed boundary conditions on Lorentzian timefolds to expand the causal wedge as far as the outermost extremal surface. As a corollary, we establish the Simple Entropy proposal for the holographic dual of the area of a marginally trapped surface as well as a similar holographic dual for the outermost extremal surface. We find that the simple wedge is dual to a particular coarse-grained CFT state, obtained via averaging over all possible Python's lunches. An efficient quantum circuit converts this coarse-grained state into a "simple state" that is indistinguishable in finite time from a state with a local modular Hamiltonian. Under certain circumstances, the simple state modular Hamiltonian generates an exactly local flow; we interpret this result as a holographic dual of black hole uniqueness.

Figures (6)

• Figure 1: An illustration of the Python's lunch. On the left, the geometry of a Cauchy slice featuring the titular python's lunch between the two constrictions, the dominant QES $X_{\mathrm{min}}$ and the non-minimal QES $X$, both of which lie behind the causal surface $C$. On the right, a spacetime diagram of the same.
• Figure 2: A caricature of the procedure used to push the causal wedge towards the appetizer in JT gravity coupled to a classical massless scalar. The leftmost panel is the original spacetime including left- and right-movers with reflecting boundary conditions. The causal surface of the right boundary is $C_{1}$. In the middle panel, the left movers have been turned off, which causes the future event horizon to shift inwards. The resulting causal surface is $C_{2}$, which is null-separated from $C_{1}$. The final panel shows that the right movers have been turned off, which causes the past event horizon to move inwards, shifting the causal surface to $C_{3}$. This shift reveals new left-movers in the causal wedge, which will have to be removed in subsequent zigzags along the past and future event horizons.
• Figure 3: The coarse-graining procedure of EngWal17bEngWal18 as applied to the outermost extremal surface. The spacetime behind the outermost extremal surface $X$ is discarded and replaced with a CPT conjugate of the outermost extremal wedge. The rest of the spacetime is generated by standard Cauchy evolution.
• Figure 4: An illustration of the approach to the limit point $C_{\mathrm{lim}}$, where $C_{A}$ and $C_{B}$ are infinitesimally close to the limiting point.
• Figure 5: On the left: three-dimensional (left) illustration of the past ($v=0$) and future ($u=0$) event horizons, with a slicing of the future event horizon given by the intersection of $u=0$ with past causal horizons originating from complete slices of the $\mathscr{I}$. On the right: a conformal diagram illustrating the same.

Theorems & Definitions (13)

• Proposition 1
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Definition 1
• Definition 2
• Lemma 4