We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at… (More)

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We… (More)

Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum… (More)

Assuming that the world-sheet sigma-model in the AdS/CFT correspondence is an integrable quantum field theory, we deduce that there might be new corrections to the spin-chain/string Bethe ansatz… (More)

The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential fall off of the 2-point function with geodesic distance determines the fractal… (More)

We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian spacetimes, each possessing a unique Wick… (More)

We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We… (More)

We show that lattice regularization of noncommutative field theories can be used to study non-perturbative vacuum phases. Specifically we provide evidence for the existence of a striped phase in… (More)

The express purpose of these Lecture Notes is to go through some aspects of the simplicial quantum gravity model known as the Dynamical Triangulations approach. Emphasis has been on lying the… (More)