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Brick Walls for Black Holes in AdS/CFT

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.