Holographic description of quantum black holes and space-time

We study the microscopic structure of black holes and curved space-time through the gravity/gauge theory duality. Large N DO-braves have two different dual descriptions: Schwarzschild black hole on warped AdS ₂ × S8 geometry, and finite-temperature strongly-coupled gauge quantum mechanics in 0 + 1 dimensions. We work directly in the strongly-coupled quantum mechanics using a mean-field approximation to describe the black hole non-perturbatively. Using a D0-brave as a probe, we obtain the distribution of masses of W-bosons, which represent virtual open strings between the probe and the background black hole. We find a clear separation between light and heavy states as the probe approaches the horizon, and light states are thermally excited at the stringy stretched horizon. This shows that the light states correspond to black hole degrees of freedom and the heavy states correspond to the degrees of freedom of whole AdS space. Effective potential for the probe agrees with supergravity expectations, and the entropy analysis of the probe shows that the stretched horizon of the black hole arises dynamically in the gauge theory, as thermal restoration of unbroken U(N + 1) gauge symmetry.; The light states have an effective description by a gas of non-interacting quasi-particles living on the stretched horizon. This simple model is shown to account for not only many of the static thermodynamic properties but also dynamical properties of the black hole. We use this model to show that the entropy of the quantum mechanics is proportional to the black hole horizon area in Planck units. We generalize this quasi-particle description of D0-brave black hole to a large class of black holes including the BTZ black hole, and also to the de-Sitter space cosmological horizon. We also comment on the situation where quasi-particle description is invalid.; Finally we study how these two D0-brane descriptions are modified if we put D0-branes on non-trivial anti-pp-wave background. We study this effect from both gravity and gauge theory point of view, and find the both deformations to gravity and gauge theory are consistent. We also study the other holographic theory, called “M(atrix) model” as M-theory on general pp-wave backgrounds.