A proposal of the gauge theory description of the small Schwarzschild black hole in AdS${}_5\times$S${}^5$

Abstract

Based on 4d $\mathcal{N}=4$ SYM on ${\mathbb{R}}^1\times$S${}^3$, a gauge theory description of a small black hole in AdS${}_5\times$S${}^5$ is proposed. The change of the number of dynamical degrees of freedom associated with the emission of the scalar fields' eigenvalues plays a crucial role in this description. By analyzing the microcanonical ensemble, the Hagedorn behavior of long strings at low energy is obtained. Modulo an assumption based on the AdS/CFT duality for a large black hole, the energy of the small ten-dimensional Schwarzschild black hole $E\sim 1/(G_{10,\mathrm{N}}{T}^7)$ is derived. A heuristic gauge theory argument supporting this assumption is also given. The same argument applied to the ABJM theory correctly reproduces the relation for the eleven-dimensional Schwarzschild black hole. One of the consequences of our proposal is that the small and large black holes are very similar when seen from the gauge theory point of view.

16 pages, 8 figures. A few corrections in equations and logic have been added to section 3. The result remains unchanged

References in corpus (6)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Lumpy AdS${}_5\times$ S${}^5$ Black Holes and Black Belts
• Small AdS black holes from SYM
• On the shape of a D-brane bound state and its topology change
• Cascade of Gregory-Laflamme Transitions and U(1) Breakdown in Super Yang-Mills
• Deconfinement transition as black hole formation by the condensation of QCD strings

Cited by in corpus (4)

• Page Curve and the Information Paradox in Flat Space
• Anatomy of Deconfinement
• Large $N$ phase transitions and the fate of small Schwarzschild-AdS black holes
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$