Supersymmetric Spectral Form Factor and Euclidean Black Holes

TL;DR

This paper investigates the late-time spectral form factor in 4D super Yang-Mills theory, revealing how multi-cut saddle points related to Euclidean black holes dominate at late times, preventing decay and providing a geometric interpretation of the ramp.

Contribution

It introduces a novel analysis of the spectral form factor in super Yang-Mills theory, connecting multi-cut saddle points to Euclidean black holes and the ramp in spectral statistics.

Findings

Late-time behavior governed by multi-cut saddles.

Multi-cut saddles correspond to orbifolded Euclidean black holes.

Prevents spectral form factor decay at late times.

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.