SciPost Submission Page
Geometric Surprises in the Python's Lunch Conjecture
by Gurbir Arora, Matthew Headrick, Albion Lawrence, Martin Sasieta, Connor Wolfe
Submission summary
| Authors (as registered SciPost users): | Martin Sasieta |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2401.06678v2 (pdf) |
| Date submitted: | 2024-03-11 13:14 |
| Submitted by: | Sasieta, Martin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the python's lunch conjecture of Brown et al., the bulge's area controls the complexity of bulk reconstruction, in the sense of the amount of post-selection that needs to be overcome for the reconstruction of the entanglement wedge beyond the outermost extremal surface. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as Ryu-Takayanagi surfaces: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; and they probe entanglement shadows, orbifold singularities, and compact spaces such as the sphere in AdS$_p\times S^q$. These features imply, according to the python's lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity pleateaus after a certain number of boundaries have been included.
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The paper investigates properties of bulge surfaces using Almgren-Pitts min-max theory. Bulge surfaces are non-minimal extremal surfaces of codimension 2 surfaces that lie between candidate RT surfaces. Their importance resides in their (conjectured) role of assigning a complexity to the holographic map between operators to one side of the surface and the dual operators on the holographic boundary. This warrants the further investigation of bulge surfaces.
The paper uses Almgren-Pitts (AP) theory to define the bulge surface. Application of AP theory shows that between any two locally minimal surfaces (the candidate RT surfaces) there exits a third extremal surface with Morse index one, indicating the one direction along which the second derivative of the area decreases. This is how the paper defines a bulge surface.
The scope of the paper is limited to time symmetric slices of spacetimes that admit them and focuses on areas instead of generalized entropy. Yet, there are several noteworthy results. The most interesting to me are how bulge surfaces need not respect the symmetry of the background spacetime (and hence of the boundary quantum state) and that they can probe the internal space. The paper has additional important results in finding bulge surfaces in horizonless situations and multi boundary wormholes.
My only suggested edit is to correct one wrong sentence in the introduction (second to last paragraph of page 3). The sentence claims that the QES is relevant only when the bulk entanglement is 1/Gn. The correct statement is that QES is relevant when the derivative of the matter entropy competes with the derivative of the area, which can happen even with small bulk matter entanglement. Provided this point is addressed, I recommend the paper for publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Report
In gravitational holography, access to a subregion of the boundary theory in principle allows the reconstruction of a part of the bulk spacetime called the entanglement wedge. However, for part of the entanglement wedge, this reconstruction may be very complex. It has been conjectured that this complexity may be quantified using “bulge surfaces”, which are certain non-minimal extremal surfaces in the bulk spacetime. Motivated by this conjecture, the paper provides a thorough study of the geometry of bulge surfaces on time reflection symmetric Cauchy slices of classical holographic spacetimes and finds quite a few interesting features.
I find the paper very well-written and interesting. The geometric questions addressed are directly relevant for current efforts to understand the role of complexity in gravitational physics. The paper is clear about the simplifying assumptions that are made. It is useful that the properties of bulge surfaces are illustrated using many relevant examples. Some of the features found make striking predictions for the complexity of bulk reconstruction (although it does not seem straightforward to test those predictions directly). And a number of interesting questions for future research are raised in the discussion. I recommend that the paper be published.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)