This series consists of talks in the area of Quantum Gravity.
In this talk, I will describe the framework of large D matrix models, which provides new limits for matrix models where the sum over planar graphs simplifies when D is large. The basic degrees of freedom are a set of D real matrices of size NxN which is invariant under O(D). These matrices can be naturally interpreted as a real tensor of rank three, making a compelling connection with tensor models. Furthermore, they have a natural interpretation in terms of D-brane constructions in string theory.
According to the Asymptotic Safety conjecture, a (non-perturbatively)
renormalizable quantum field theory of gravity could be constructed
based on the existence of a non-trivial fixed point of the
renormalization group flow.
The existence of this fixed point can be established, e.g., via the
non-perturbative methods of the functional renormalization group (FRG).
In practice, the use of the FRG methods requires to work within
truncations of the gravitational action, and higher-derivative operators
Hopf algebra lattice models are related to certain topological quantum field theories and give rise to topological invariants of oriented surfaces. Examples are the combinatorial quantisation of Chern-Simons theory and the Kitaev model.
In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus break unitarity. Here we show that these expectations can be made precise in loop quantum cosmology.
Cosmological perturbation theory has a long tradition for describing the early phases of the Universe. As the observations of the CMB radiation suggest, it is reasonable, at least as a first approximation, to implement cosmological inhomogeneities as small perturbations around homogeneous and isotropic FRW solutions. In these approaches, backreactions between the inhomogeneities and the background are usually neglected. There is an ongoing debate about how and to which extend these backreactions affect the large scale structure of the Universe.
I will explain how dark energy in cosmology could arise from the
noisy diffusion of energy from the low energy degrees of freedom of matter (described in terms of QFT)
to the fundamental Planckian granularity (expected from quantum gravity). This
perspective leads to a natural model resolving the fine tuning problem associated to the small
value of the cosmological constant. However, recent observations suggest that the dark energy
component in our universe might not be constant and should instead have grown from the recombination time to the present.
It has long been argued that combining the uncertainty principle with gravity will lead to an effective minimum length at the Planck scale. A particular challenge is to model the presence of a smallest length scale in a manner which respects continuous spacetime symmetries. One path for deriving low-energy descriptions of an invariant minimum length in quantum field theory is based on generalized uncertainty principles. Here I will consider the question how this approach enables one to retain Euclidean or even Lorentzian symmetries.
We study dimensionally restricted non-perturbative causal set quantum dynamics in two and three spacetime dimensions with non-trivial global spatial topology. The causal set sample space is generated from causal embeddings into latticisations of flat background spacetimes with global spatial topology and
The asymptotic symmetry charge algebra of certain class of spacetimes could have a nontrivial central extension, which measures the non-equivariance of the charges of the large gauge transformations. The Cardy formula of the dual CFT has been famously used to derive black hole entropy. However, it remains obscure from the point of view of gravity why such a constant on the gravitational phase space could encode the information about the density of black hole micro-states, and what the degrees of freedom accounting for the black hole entropy truly are.
Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phenotypes, niches, ecosystems. We wish to argue that the evolution of life marks the end of a physics world view of law entailed dynamics.