Holographic complexity, as the bulk dual of quantum complexity, encodes the geometric structure of black hole interiors. Motivated by the complexity=anything proposal, we introduce the spectral representation for generating functions associated with codimension-one and codimension-zero holographic complexity measures. These generating functions exhibit a universal slope-ramp-plateau structure, analogous to the spectral form factor in chaotic quantum systems. In such systems, quantum complexity evolves universally, displaying long-time linear growth followed by saturation at late times. By employing the generating function formalism, we demonstrate that this universal behavior originates from random matrix universality in spectral statistics and from a particular pole structure of the matrix elements of the generating functions in the energy eigenbasis. Using the residue theorem, we prove that the existence of this pole structure is both a necessary and sufficient condition for the linear growth of complexity measures. Furthermore, we show that the late-time saturation plateau arises directly from the spectral level repulsion, a hallmark of quantum chaos.

Biography

Shan-Ming Ruan is an Assistant Professor at the Institute of Theoretical Physics in the School of Physics at Peking University. He received his PhD from Perimeter Institute for Theoretical Physics and the University of Waterloo in 2021, his M.S. from the Institute of Theoretical Physics, Chinese Academy of Sciences, and his B.S. from Lanzhou University. Before joining Peking University in 2025, he held postdoctoral positions at Kyoto University and Vrije Universiteit Brussel. His research focuses on black hole physics, holographic duality, and quantum gravity.

Inviter: Shao-Jiang Wang