A Note on Black Hole Entropy in Loop Quantum Gravity

TL;DR

This paper explores how choosing an imaginary Barbero-Immirzi parameter in loop quantum gravity may connect black hole entropy calculations to boundary conformal field theories, potentially matching the Bekenstein-Hawking entropy.

Contribution

It proposes a speculative link between boundary conformal field theories and black hole entropy in loop quantum gravity with an imaginary Barbero-Immirzi parameter.

Findings

Boundary conformal field theory density of states matches Bekenstein-Hawking entropy

Suggests a simplified approach to black hole thermodynamics in loop quantum gravity

Provides background and speculation on conformal field theories at horizons

Abstract

Several recent results have hinted that black hole thermodynamics in loop quantum gravity simplifies if one chooses an imaginary Barbero-Immirzi parameter $\gamma=i$. This suggests a connection with $\mathrm{SL}(2,\mathbb{C})$ or $\mathrm{SL}(2,\mathbb{R})$ conformal field theories at the "boundaries" formed by spin network edges intersecting the horizon. I present a bit of background regarding the relevant conformal field theories, along with some speculations about how they might be used to count black hole states. I show, in particular, that a set of unproven but plausible assumptions can lead to a boundary conformal field theory whose density of states matches the Bekenstein-Hawking entropy.