On the Role of Chaos in the AdS/CFT Connection
S. Kalyana Rama, B. Sathiapalan
TL;DR
This work proposes that chaotic self-thermalization in the boundary Yang-Mills theory under the AdS/CFT correspondence explains how infalling pure-state configurations appear at finite temperature, corresponding to black hole formation in the bulk. By analyzing a dilaton wave equation in the AdS$_5$-Schwarzschild background and imposing ingoing boundary conditions at the horizon, the authors show that the associated energy eigenvalues are generically complex, yielding a damping rate $\gamma$ that scales with temperature and depends on momentum; this damping is identified with the Lyapunov exponent of classical Yang-Mills and links to self-thermalization. Although explicit numerical values require solving the eigenvalue problem, the qualitative behavior—$\gamma$ decreasing with increasing $k^2$ and remaining nonzero due to horizon drag—is consistent with chaotic YM simulations and supports a qualitative, holographic mechanism for black-hole thermality. The paper thus provides a framework to quantitatively connect a bulk supergravity calculation to boundary quantum chaos and finite-temperature behavior, suggesting concrete cross-checks with YM damping rates and lattice results.
Abstract
The question of how infalling matter in a pure state forms a Schwarzschild black hole that appears to be at non-zero temperature is discussed in the context of the AdS/CFT connection. It is argued that the phenomenon of self-thermalization in non-linear (chaotic) systems can be invoked to explain how the boundary theory, initially at zero temperature self thermalizes and acquires a finite temperature. Yang-Mills theory is known to be chaotic (classically) and the imaginary part of the gluon self-energy (damping rate of the gluon plasma) is expected to give the Lyapunov exponent. We explain how the imaginary part would arise in the corresponding supergravity calculation due to absorption at the horizon of the black hole.