Codimension-Zero Holographic Complexity and Spectral Three-Point Correlators

@misc{miyaji2026codimensionzero,
  title = {{Codimension-Zero Holographic Complexity and Spectral Three-Point Correlators}},
  author = {Masamichi Miyaji and Shan-Ming Ruan and Shono Shibuya and Kazuyoshi Yano},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13289},
  eprint = {2610.13289},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13289},
}

TY  - UNPB
TI  - Codimension-Zero Holographic Complexity and Spectral Three-Point Correlators
AU  - Masamichi Miyaji
AU  - Shan-Ming Ruan
AU  - Shono Shibuya
AU  - Kazuyoshi Yano
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13289
UR  - https://arxiv.org/abs/2610.13289
AB  - Holographic complexity is expected to capture the linear growth of black hole interiors, with quantum corrections ultimately leading to a late-time saturation. We develop a spectral formulation of holographic complexity measures associated with codimension-zero bulk regions in the framework of the complexity=anything proposal. The corresponding generating function of complexity is governed by three-point correlation functions of the density of states, establishing a direct connection between bulk geometric observables and nonperturbative Euclidean spacetime wormholes. We find that the codimension-zero holographic complexity reduces to the sum of two codimension-one contributions and exhibits a universal time evolution, characterized by an exponentially long regime of linear growth followed by saturation at the Heisenberg time. The late-time plateau is a direct result of the spectral level repulsion, a generic feature of quantum chaotic systems, thereby providing a universal mechanism for the saturation of holographic complexity. We also develop a complementary operator interpretation, in which Euclidean wormhole corrections render the semiclassical basis of fixed-complexity states overcomplete. Constructing a complete orthonormal basis then yields well-defined holographic complexity operators that reproduce the same universal time evolution. Our results establish a unified connection among black hole interiors, chaotic spectral statistics, and Euclidean wormholes in quantum gravity.
ER  -