Integrability vs. Information Loss: A Simple Example

TL;DR

This paper explores how integrable structures in Yang-Mills theory relate to information loss in gravity, showing that coarse measurements cannot distinguish microstates due to Planck-scale limitations.

Contribution

It demonstrates that integrable conserved charges in the dual gravitational description are inaccessible to semiclassical observers, linking integrability to information loss.

Findings

Conserved charges can be measured via asymptotic multipole moments.

Planck-scale precision is needed to distinguish microstates.

Semiclassical measurements lead to information loss about quantum states.

Abstract

The half-BPS sector of Yang-Mills theory with 16 supercharges is integrable: there is a set of commuting conserved charges, whose eigenvalues can completely identify a state. We show that these charges can be measured in the dual gravitational description from asymptotic multipole moments of the spacetime. However, Planck scale measurements are required to separate the charges of different microstates. Thus, semiclassical observers making coarse-grained measurements necessarily lose information about the underlying quantum state.