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 shows the divergence due to the large degenerate states near the horizons. After studying the universal nature of the divergence in various holographic settings 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.
Highlights
Understanding the quantum nature of gravity has been one of the most exciting topics in high energy physics, and black holes are touchstones of our understanding of the quantum nature of gravity
First we study the universal nature of the brick wall model in various exotic black brane backgrounds for the probe fields
Even after the SU(N ) QCD like theory shows the confinement–deconfinement transition. This contradicts the gravity analysis; if we consider the free energy of the bulk scalar field, which is dual to the gauge singlet field, it shows the divergence without the brick wall cut-off due to the near horizon throats in the vicinity of the black holes with h = 0
Summary
Understanding the quantum nature of gravity has been one of the most exciting topics in high energy physics, and black holes are touchstones of our understanding of the quantum nature of gravity. We interpret the Planck-scale cut-off dependence of the brick wall models as the large N dependence of the free energy of the probe fields These analyses suggest us that in dual field theory, it is difficult to have a gauge-free singlet object unless it is a composite object. The organization of this paper is the following; In Section 2, we briefly review the known results about the original brick wall model for black holes by ’t Hooft and see the probe field free energy show divergence due to the near horizon regime. We mainly consider the probe field added on top of above black holes and discuss mainly the implication of the probe field free energy divergence and its connection to dual field theory degrees of freedom
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