Integrability vs. Information Loss: A Simple Example

TL;DR

Balasubramanian et al. address how integrability in the half-BPS sector of ${ m SU}(N)$ Yang–Mills with 16 supercharges coexists with information loss in the gravitational dual. They show that the higher conserved charges $M_k$ are encoded in the angular multipole moments of the dual LL(M) gravity solutions, so a full quantum description preserves integrability while coarse-grained semiclassical observers access only the lowest multipoles. Consequently, almost all microstates are indistinguishable at semiclassical accuracy, and distinguishing them requires Planck-scale precision $(l_p)$. The work highlights a sharp UV/IR interplay in AdS/CFT and demonstrates that information remains in quantum gravity even when the classical geometry appears universal.

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.