Supersymmetric Spectral Form Factor and Euclidean Black Holes

Sunjin Choi; Seok Kim; Jaewon Song

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arXiv · 2206.15357

Supersymmetric Spectral Form Factor and Euclidean Black Holes

Sunjin Choi·Seok Kim·Jaewon Song

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Abstract

The late-time behavior of spectral form factor (SFF) encodes the inherent discreteness of a quantum system, which should be generically non-vanishing. We study an index analog of the microcanonical spectrum form factor in four-dimensional $\mathcal{N}=4$ super Yang-Mills theory. In the large $N$ limit and at large enough energy, the most dominant saddle corresponds to the black hole in the AdS bulk. This gives rise to the slope that decreases exponentially for a small imaginary chemical potential, which is a natural analog of an early time. We find that the `late-time' behavior is governed by the multi-cut saddles that arise in the index matrix model, which are non-perturbatively sub-dominant at early times. These saddles become dominant at late times, preventing the SFF from decaying. These multi-cut saddles correspond to the orbifolded Euclidean black holes in the AdS bulk, therefore giving the geometrical interpretation of the `ramp.' Our analysis is done in the standard AdS/CFT setting without ensemble average or wormholes.

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Sunjin Choi, Seok Kim, Jaewon Song. 2022-06-30. Supersymmetric Spectral Form Factor and Euclidean Black Holes. https://arxiv.org/abs/2206.15357

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