Geometric surprises in the Python's lunch conjecture

• DOI: 10.21468/scipostphys.16.6.152
• Publication Date: 2024-06-12T11:43:18Z
• Authors: Gurbir Arora; Matthew Headrick; Albion Lawrence; Martin Sasieta; Connor Wolfe
• Keywords: High Energy Physics - Theory; High Energy Physics - Theory (hep-th); Physics; QC1-999; 0103 physical sciences; 500; FOS: Physical sciences; 530; 01 natural sciences

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× S^qp×Sq. 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.