Quantum Spacetime and Gravity in Matrix Models at one Loop

Reconciling gravity with quantum mechanics remains to be one of the major open problems in theoretical physics. It is widely expected that this leads to a quantum structure of space-time at short distances, which requires a new framework to formulate physical theories. One promising such framwork is given by certain matrix models, which can be viewed as an alternative approach to string theory. Certain solutions of this model provide a quantized cosmological space-time, and its fluctuations provide all the ingredients for gravity. In particular, it was found recently that the dynamics of this emergent gravity theory is governed by an effective action which is similar to the one in general relativity (GR), which is the accepted description of classical gravity. However, the matrix model leads to deviations from GR which are expected to be important on cosmic scales, as well as extra degrees of freedom whose physical significance remains to be understood. The aim of this project is to study and elaborate this emergent gravity theory in detail, and to compare it with general relativity. The first step towards this goal will be a detailed elaboration of the effective action, which results from quantum effects in the matrix model. The leading contribution of these quantum effects known as one-loop contribution will be elaborated in detail. This provides the starting point for a systematic analysis of the regime where the emergent gravity is close to GR, as well as the regime where it differs significantly from GR. The cross-over between these regimes will be studied, and the physical implications of the extra degrees of freedom will be clarified. In particular, spherically symmetric vacuum solutions will be studied taking into account these quantum effects, and their relation with the Schwarzschild geometry will be elaborated. Further objectives include stabilization of fuzzy extra dimensions due to vacuum energy, which is important in the framework. Finally, we will attempt to understand the singularity resolution in the center of black holes within the matrix model framwork.