On non-perturbative quantum gravity: Holography and matrix models in string theory.

摘要

After a decades-long search for a theory of quantum gravity, the holographic principle has emerged as a framework to unify the independent successes of string theory and black hole thermodynamics. For the first time, some of the most vexing questions of quantum gravity can be tackled in a well-controlled environment. After reviewing the progression from perturbative string theory and black hole thermodynamics to the holographic principle, we apply the most basic realizations of holography, the matrix models, toward understanding non-perturbative issues of quantum gravity. Using the LLM matrix model dual to a sector of Type IIB string theory, we examine topology change of spacetime, where the geometric description is seen to break down in favor of more fundamental fermion fluid degrees of freedom. Next, we examine a class of spacetime singularities which arise as the extremal limit of a family of black holes. We show that the singularities emerge upon coarse-graining over smooth microstate geometries, shedding light on the connection between geometry and thermodynamics. Lastly, we use the BFSS matrix model to explore the emergence of non-perturbative gravitational degrees of freedom from non-commutative geometry.