This series consists of talks in the area of Quantum Gravity.
We prove that the $\lambda\phi^4_4$ quantum field theory on noncommutative Moyal space is, in the limit of infinite noncommutativity, exactly solvable in terms of the solution of a non-linear integral equation. The proof involves matrix model techniques which might be relevant for 2D quantum gravity and its generalisation to coloured tensor models of rank $\geq 3$.
The authors have revealed a fundamental structure which has been hidden within the Wheeler-DeWitt (WDW) constraint of four dimensional General Relativity (GR) of Lorentzian signature in the Ashtekar self-dual variables. The WDW equation can be written as the commutator of two geometric entities, namely the imaginary part of the Chern-Simons functional Q and the local volume element V(x) of 3-space.
Thermodynamical aspects of gravity have been a tantalising puzzle for more than forty years now and are still at the center of much activity in semiclassical and quantum gravity. We shall explore the possibility that they might hint toward an emergent nature of gravity exploring the possible implications of such hypothesis. Among these we shall focus on the possibility that Lorentz invariance might be only a low energy/emergent feature by discussing viable theoretical frameworks, present constraints and open issues which make this path problematic.
I will describe the relationship between radiated energy and entanglement entropy of massless fields at future null infinity (the "Page curve") in two-dimensional models of black hole evaporation. I will use this connection to derive a general feature of any unitary-preserving evaporation scenario: the Bondi mass of the hole must be non-monotonic. Time permitting, I will comment on time scales in such scenarios.
Locally covariant quantum field theory (LCQFT) has proven to be a very successful framework for QFT on curved spacetimes. It is natural to ask, how far these ideas can be generalized and if one can learn something about quantum gravity, using LCQFT methods. In particular, one can use the relative Cauchy evolution to formulate the notion of background independence. Recently we have proven that background independence in this sense holds for effective quantum gravity, formulated as a perturbative QFT.
After the seminal work of Connes and Tretkoff on the Gauss-Bonnet theorem for the noncommutative 2-torus and its extension by Fathizadeh and myself, there have been significant developments in understanding the local differential geometry of these noncommutative spaces equipped with curved metrics. In this talk, I will review a series of joint works with Farzad Fathizadeh in which we compute the scalar curvature for curved noncommutative tori and prove the analogue of Weyl's law and Connes' trace theorem.
We study the classical constraint algebra of Hořava-Lifshitz gravity, where due to the breaking of 4d diffeomorphism symmetry, there is a new dimensionless coupling absent in GR and whose role is not yet clear. Starting from two apparently contradictory results, we show how the role of the extra coupling differs between the projectable and non-projectable versions of the theory. In particular, we see how in the latter, it gives rise to a non-trivial constraint algebra, akin to the conditions seen in the CMC gauge of GR.
Rank 3 tensorial group fields theories with gauge invariance condition appear to be renormalizable on dimension 3 groups such as SU(2), but also on dimension 4 groups. Building on an analogy with ordinary scalar field theories, I will generalize such models to group dimension 4 - ε, and discuss what this might teach us about the physically relevant SU(2) case.
Arguments that gravity cannot be a local renormalizable quantum field theory come from both field theory lore and black hole physics. Two current approaches to quantum gravity, asymptotic safety and Horava-Lifshitz gravity, both of which treat quantum gravity as a local renormalizable QFT, are explicitly constructed to counter field theory arguments about the non-renormalizability of gravity. However, any proposed renormalizable theory of quantum gravity must also answer black hole physics based counter-arguments.
Lorentz invariance is considered a fundamental symmetry of physical theories. However, while Lorentz violations are strongly constrained in the matter sector, constraints in the gravitational sector are weaker, allowing to contemplate the idea of Lorentz-violating gravity theories.