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arXiv · 2610.13289

Codimension-Zero Holographic Complexity and Spectral Three-Point Correlators

Masamichi Miyaji·Shan-Ming Ruan·Shono Shibuya·Kazuyoshi Yano
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Abstract

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.

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Masamichi Miyaji, Shan-Ming Ruan, Shono Shibuya, Kazuyoshi Yano. 2026-10-09. Codimension-Zero Holographic Complexity and Spectral Three-Point Correlators. https://arxiv.org/abs/2610.13289

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