Quantum Gravity

I will describe recent work in collaboration with Adam
Henderson, Alok Laddha, and Madhavan Varadarajan on the loop quantization of a
certain $G_{\mathrm{N}}\rightarrow 0$ limit of Euclidean gravity, introduced by
Smolin. The model allows one to test various quantization choices one is faced
with in loop quantum gravity, but in a simplified setting.  The main results are the construction of
finite-triangulation Hamiltonian and diffeomorphism constraint operators whose
continuum limits can be evaluated in a precise sense, such that the quantum

I
will describe a discrete model of spacetime which is quantum-mechanical,
causal, and background free. The kinematics is described by networks whose
vertices are labelled with arrows. These networks can be evolved forwards (or
backwards) in time by using unitary replacement rules. The arrow structure
permits one to define dynamics without using an absolute time parameter.
 Based on arXiv:1201.2489.

Causal
Dynamical Triangulations” (CDT) is a lattice theory where aspects of quantum
gravity can be studied. Two-dimensional CDT can be solved analytically and the
continuum (quantum) Hamiltonian obtained.

In this talk I will show that this continuum Hamiltonian is the one obtained by
quantizing two-dimensional projectable Horava-Lifshitz gravity.

Both AdS/CFT duality and more general reasoning from quantum gravity point to a rich collection of boundary observables that always evolve unitarily. The physical quantum gravity states described by these observables must be solutions of the spatial diffeomorphism and Wheeler-deWitt constraints, which implies that the state space does not factorize into a tensor product of localized degrees of freedom.