Quantum Gravity

The functional renormalization group is a tool in the systematic search for Euclidean QFTs that works with very little input: All one needs to specify is a field content, symmetries and a notion of locality. The functional renormalization group then allows one to scan this theory space for bare actions for which the path integral can be performed nonperturbatively. These actions appear as fixed points (and relevant deformations) of the renormalization group flow (so-called asymptotic safety). Such a systematic search has so far not been performed for the tensor model approach to quantum gravity. We investigate matrix models for 2-dimensional gravity and the Grosse-Wulkenhaar model, which is a simple tensor model for a 4D noncommutative scalar field theory, as a first step. I will report on work, done in collaboration with Astrid Eichhorn and Alessandro Sfondrini, where we confirmed asymptotic safety purely through functional RG methods. Based on the lessons learned from these models I will summarize how the usual continuum RG approach has to be generalized for the investigation of tensor models and conclude with a recipe for the investigation of general tensor models.

The late physicist John Wheeler, was renowned for his Socratic method of conducting physics discussions. "Why is general relativity the way it is? What makes it special?" were reportedly questions one should expect in his presence. There are different answers to these questions, each requiring a set of assumptions - which Wheeler would likely question again - and each bringing with it new insights into physics as a whole. This talk will put forward new principles for deriving general relativity. Perhaps more than is the case with other construction principles, the principles introduced are not limited to the derivation of general relativity, requiring only an specification of the theory's phase space in order to be applicable. To be less enigmatic, one defines observable equivalence between physical theories in the Dirac constraint setting, and then the principle merely searches theory space for two equivalent (or dual) fully constrained theories. We find it quite remarkable that such a complex theory as general relativity emerges, when no initial presupposition even on the existence of space-time is made. If there is time (and I will argue there is!) I will discuss another issue that also distinguishes the present set of assumptions: the possibility that they are in a concrete sense ``self-selected", which I like to think would be more satisfactory to Wheeler's line of questioning (or at least give him more to chew on).

AdS/CFT is a duality relating the degrees of freedom in a D dimensional bulk gravity theory to a (D-1) dimensional theory living on the boundary. I will argue that in fact the boundary theory contains only a subset of the bulk observables. For each state of the boundary theory, there are multiple bulk states dual to it, which can be operationally distinguished by observers who fall across event horizons. Based on arXiv:1210.3590.

We argue that the scale-free spectrum that is observed in the cosmic microwave background is the result of a phase transition in the early universe.  The observed tilt of the spectrum, which has been measured to be 0.04, is shown to be equal to the anomalous scaling dimension of the correlation function.  The phase transition replaces inflation as the mechanism that produces this spectrum. The tilt further indicates that there is a fundamental small length scale in nature that we have not yet observed in any other way.

A defining feature of holographic dualities is that, along with the bulk equations of motion, boundary correlators at any given time t determine those of observables deep in the bulk. We argue that this property emerges from the bulk gravitational Gauss law together with bulk quantum entanglement as embodied in the Reeh-Schlieder theorem. Stringy bulk degrees of freedom are not required and play little role even when they exist. As an example we study a toy model whose matter sector is a free scalar field. The energy density (\rho) sources what we call a pseudo-Newtonian potential (\Phi) through Poisson's equation on each constant time surface, but there is no back-reaction on the matter. We show the Hamiltonian to be essentially self-adjoint on the domain generated from the vacuum by acting with boundary observables localized in an arbitrarily small neighborhood of the chosen time t. Since the Gauss law represents the Hamiltonian as a boundary term, the model is holographic in the sense stated above.

Binary pulsars are excellent laboratories to test the building blocks of Einstein's theory of General
Relativity. One of these is Lorentz symmetry which states that physical phenomena appear the same for all inertially moving observers. We study the e ect of violations of Lorentz symmetry in the orbital evolution of binary pulsars and that it induces a much more rapid decay of the binary's orbital period due to the emission of dipolar radiation. The absence of such behavior in recent observations allows us to place the most stringent constraints on Lorentz violation in gravity, thus verifying one of the cornerstones of Einstein's theory much more accurately than any previous gravitational observation.

Recently powerful techniques have emerged for performing multi-loop computations of scattering amplitudes in quantum gravity and  supergravity.  These techniques include generalized unitarity and the double-copy property, related to color-kinematics duality in gauge theory.  Using these  techniques, the ultraviolet divergence structure of N=8 supergravity, and more recently pure N=4 supergravity, have been assessed, not only in four space-time dimensions but also in higher dimensions.  The results can be compared to expectations based on potential counterterms that can be constructed using (conjectured) superspace formalisms or nonlinear symmetry constraints.  Interestingly, the critical ultraviolet dimension in which N=8 supergravity first diverges is equal to that for N=4 super-Yang-Mills theory through four loops.  If this statement were to hold to all loop orders, then N=8 supergravity would represent a perturbatively finite, point-like theory of quantum gravity in four dimensions.  In this talk, I will review all of this recent progress.

Causal dynamical triangulations (CDT) define a nonperturbative path integral for quantum gravity as a sum over triangulations. Causality is enforced on the kinematical level by means of a preferred
foliation.

In this talk I present a new model of dynamical triangulations based on Lorentzian building blocks, where the triangulations in general do not have such a preferred foliation. The essential ingredients of the new model are a local causality constraint and a consistency condition on the global flow of time. After a compact review on CDT I discuss the theoretical aspects of the new model in 1+1 and 2+1 dimensions, followed by a presentation of numerical results in 2+1 dimensions. These results show that the new model and CDT have similar long-distance properties in 2+1 dimensions.

By way of presenting some classic and many new results, my talk will indulge shamelessly in
advertising "Causal Dynamical Triangulations (CDT)" as a hands-on approach to nonperturbative quantum gravity that reaches where other approaches currently don't. After summarizing the rationale and basic ingredients of CDT quantum gravity and some of its key findings (like the emergence of a classical de Sitter space), I will focus on some very recent results: how we uncovered the presence of a second-order phase transition (so far unique in 4D quantum
gravity), news on the controversy between doing things the Lorentzian or the Euclidean way, and new results on the role of the preferred time slicing in CDT - all hopefully worth your while!

Effective field theory techniques allow reliable quantum calculations in general relativity at low energy. After a review of these techniques, I will discuss the attempts to define the gravitational corrections to running gauge couplings and to the couplings of gravity itself. I will also describe an attempt to understand the relation between the effective field theory and Asymptotic Safety in the region where they overlap.

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 Dirac algebra of constraints closes nontrivially and free of anomalies.  The construction relies heavily on techniques of Thiemann's QSD treatment, and lessons learned applying such techniques to the loop quantization of parameterized scalar field theory and the diffeomorphism constraint in loop quantum gravity.  I will also briefly discuss the status of the quantum constraint algebra in full LQG, and how some of the lessons learned from the present model may guide us in that setting.

I present a candidate for a new derivation of black hole entropy. The key observation is that the action of General Relativity in bounded regions has an imaginary part, arising from the boundary term. The formula for this imaginary part is closely related to the Bekenstein-Hawking entropy formula, and coincides with it for certain classes of regions. This remains true in the presence of matter, and generalizes appropriately to Lovelock gravity. The imaginary part of the action is a versatile notion, requiring neither stationarity nor any knowledge about asymptotic infinity. Thus, it may provide a handle on quantum gravity in finite and dynamical regions. I derive the above results, make connections with standard approaches to black hole entropy, and speculate on the meaning of it all. Implications for loop quantum gravity are also discussed.