This series consists of talks in the area of Quantum Gravity.
I propose a quantum gravity model in which the fundamental degrees of freedom are pure information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration arising between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension.
I will discuss a new duality between strongly coupled and weakly coupled condensed matter systems. It can be obtained by combining the gauge-gravity duality with analog gravity. In my talk I will explain how one arrives at the new duality, what it can be good for, and what questions this finding raises.
In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation could be described by a unitary evolution without the problems encountered by standard remnant scenarios or the schemes where information is assumed to come out with the radiation while semiclassical evaporation (firewalls and complementarity).
We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordinate invariance of general relativity. Space-time fluctuations can be represented in a classical lattice gas model whose Boltzmann weights are constructed with the discretized form of the Einstein-Hilbert action.
A renormalization group transformation implements a scale transformation while resetting the UV cut-off, so that the theories before and after the RG transformation contain the same degrees of freedom, but with a modified action. In Wilson's original proposal, the cut-off is reset by integrating out the degrees of freedom between the old and new cut-off. In recent years we have learned that, alternatively, one can decouple these degrees of freedom by means of local unitary transformations (disentanglers).
We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. Assuming that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, we calculate the spectrum of scalar and tensor perturbations after the bounce, assuming initial quantum vacuum fluctuations.
Instead of formulating the state space of a quantum field theory over a single big Hilbert space, it has been proposed by Jerzy Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. I will discuss the physical motivations for this approach and explain how it can be implemented in the context of LQG. While the resulting state space forms a natural extension of the Ashtekar-Lewandowski Hilbert space, it treats position and momentum variables on equal footing.