Real Time Quantum Gravity Dynamics from Classical Statistical Yang-Mills Simulations

TL;DR

This paper uses classical lattice simulations of Yang-Mills theory to explore real-time dynamics and phase transitions related to black hole and black string configurations, revealing characteristic oscillations and potential singularity resolution.

Contribution

It introduces a novel approach to study real-time quantum gravity dynamics via classical Yang-Mills simulations, connecting phase transitions to black hole and black string topology changes.

Findings

Identification of two distinct phases linked to black hole and black string states.

Observation of damped oscillations during phase transitions, resembling quasinormal modes.

Extraction of quasinormal mode frequencies as functions of energy and N.

Abstract

We perform microcanonical classical statistical lattice simulations of SU(N) Yang-Mills theory with eight scalars on a circle. Measuring the eigenvalue distribution of the spatial Wilson loop we find two distinct phases depending on the total energy and circle radius, which we tentatively interpret as corresponding to black hole and black string phases in a dual gravity picture. We proceed to study quenches by first preparing the system in one phase, rapidly changing the total energy, and monitoring the real-time system response. We observe that the system relaxes to the equilibrium phase corresponding to the new energy, in the process exhibiting characteristic damped oscillations. We interpret this as the topology change from black hole to black string configurations, with damped oscillations corresponding to quasi-normal mode ringing of the black hole/black string final state. This would suggest that alpha' corrections alone can resolve the singularity associated with the topology change. We extract the real and imaginary part of the lowest-lying presumptive quasinormal mode as a function of energy and N.