Brick Walls for Black Holes in AdS/CFT

TL;DR

This paper investigates the divergence in free energy near black hole horizons in holographic models, attributing it to degenerate states and suggesting modifications from quantum gravity effects that impact the boundary theory's degrees of freedom.

Contribution

It provides a holographic interpretation of the brick wall divergence, linking it to boundary spectrum degeneracy and quantum gravity effects near horizons.

Findings

Divergence arises from large degeneracy of low-energy states near horizons.

Finite N effects discretize the spectrum, removing divergence.

Bulk degeneracies imply modifications to degrees of freedom counting.

Abstract

We study the 't Hooft's brick wall model for black holes in a holographic context. The brick wall model suggests that without an appropriate near horizon IR cut-off, the free energy of the probe fields show the divergence due to the large degenerate states near the horizons. After studying the universal nature of the divergence in various holographic setting in various dimensions, we interpret the nature of the divergence in a holographic context. The free energy divergence is due to the large degeneracy and continuity of the low energy spectrum in the boundary theory at the deconfinement phase. These divergence and continuity should be removed by finite N effects, which make the spectrum discrete even at the deconfinement phase. On the other hand, in the bulk, these degenerate states are localized near the horizon, and the universal divergence of these degenerate states implies that the naive counting of the degrees of freedom in bulk should be modified once we take into account the non-perturbative quantum gravity effects near the horizon. Depending on the microscopic degrees of freedom, the position, where the effective field theory description to count the states breaks down, has different Planck scale dependence. It also implies the difficulty to have an electron like gauge-singlet elementary field in the boundary theory Lagrangian. These singlet fields are at most composite fields, because they show divergent free energy, suggesting a positive power of N at the deconfinement phase.