The holographic principle and the Immirzi parameter of loop quantum gravity

TL;DR

This paper proposes a new method to determine the Immirzi parameter in loop quantum gravity by using holographic principles and the equipartition rule, suggesting a universal and holographically rooted value.

Contribution

It introduces a holographic approach to fix the Immirzi parameter, linking it to the equipartition rule and Hawking-Unruh temperature, offering a conceptual resolution to ambiguity.

Findings

Immirzi parameter can be fixed via holographic equipartition

Derived value of the Immirzi parameter has universal validity

Suggests the Immirzi parameter is rooted in the holographic principle

Abstract

The geometrical spectra in loop quantum gravity (LQG) suffer from ambiguity up to the free Immirzi parameter that is often determined by comparing results from the theory with the established dynamics at the black hole horizon. We address conceptual difficulties associated with such approaches and point out that the Immirzi parameter can be fixed naively by applying the LQG version of the equipartition rule at a holographic boundary such that the Hawking-Unruh temperature law follows. The value of the Immirzi parameter derived in this way should possess universal validity. This approach also provides a clue that this parameter could be rooted in the holographic principle.