St\"uckelberg Formulation of Holography

TL;DR

This paper proposes a holographic framework based on St"uckelberg degrees of freedom acting as qubits, explaining black hole information capacity and linking holography to quantum criticality through mode analysis.

Contribution

It introduces a novel formulation of holography using St"uckelberg fields as information carriers, connecting gauge invariance, quantum information, and critical phenomena.

Findings

St"uckelberg modes account for black hole information saturation.

The information capacity relates to the inverse gauge coupling at system scale.

A connection between holography and quantum criticality is established.

Abstract

We suggest that holography can be formulated in terms of the information capacity of the St\"uckelberg degrees of freedom that maintain gauge invariance of the theory in the presence of an information boundary. These St\"uckelbergs act as qubits that account for a certain fraction of quantum information. Their information capacity is measured by the ratio of the inverse St\"uckelberg energy gap to the size of the system. Systems with the smallest gap are maximally holographic. For massless gauge systems this information measure is universally equal to the inverse coupling evaluated at the systems' length scale. In this language it becomes very transparent why the St\"uckelberg information capacity of black holes saturates the Bekenstein bound and accounts for the entire information of the system. The physical reason is that the strength of quantum interaction is bounded from below by the gravitational coupling, which scales as area. Observing the striking similarity between the scalings of the energy gap of the boundary St\"uckelberg modes and the Bogoliubov modes of critical many-body systems, we establish a connection between holography and quantum criticality through the correspondence between these modes.