Classical Limit of Black Hole Quantum N-Portrait and BMS Symmetry

TL;DR

The paper addresses how the microscopic qubits that encode black hole entropy arise and how the classical limit of the quantum portrait relates to asymptotic symmetries. It treats the black hole as a quantum-critical condensate of $N$ soft gravitons, whose $N$ Bogoliubov-Goldstone modes carry the information and exhibit a $1/N$ energy gap; Minkowski space is modeled as a coherent state of infinite soft gravitons, linking to BMS supertranslations in the $N\to\infty$ limit. The authors identify a direct geometric interpretation: large-$N$ Goldstones correspond to BMS modes at infinity, while for finite $R$ the symmetry is broken by the horizon geometry, yielding finite-$N$ corrections that enable information recovery over finite times and induce deviations from thermality. They also discuss holographic implications of Minkowski space, the role of finite-$N$ effects for information retrieval, and possible connections to soft-graviton theorems, aiming to unify the black hole N-portrait with asymptotic symmetry approaches. The work thus provides a framework linking black hole microstates, holography, and BMS symmetry, highlighting the essential role of finite-$N$ corrections for practical information processing in black hole physics.

Abstract

Black hole entropy, denoted by N, in (semi)classical limit is infinite. This scaling reveals a very important information about the qubit degrees of freedom that carry black hole entropy. Namely, the multiplicity of qubits scales as N, whereas their energy gap and their coupling as 1/N. Such a behavior is indeed exhibited by Bogoliubov-Goldstone degrees of freedom of a quantum-critical state of N soft gravitons (a condensate or a coherent state) describing the black hole quantum portrait. They can be viewed as the Goldstone modes of a broken symmetry acting on the graviton condensate. In this picture Minkowski space naturally emerges as a coherent state of infinite-N gravitons of infinite wavelength and it carries an infinite entropy. In this paper we ask what is the geometric meaning (if any) of the classical limit of this symmetry. We argue that the infinite-N limit of Bogoliubov-Goldstone modes of critical graviton condensate is described by recently-discussed classical BMS super-translations broken by the black hole geometry. However, the full black hole information can only be recovered for finite N, since the recovery time becomes infinite in classical limit in which N is infinite.