Evidence for Asymptotic Safety

• Yannick Kluth (University of Toronto)

Room: 28B 110 In this talk I will introduce the asymptotic safety scenario for quantum gravity and the search for viable interacting fixed points. After covering the basic concepts — fixed points and their UV critical surfaces — I will explain how these are studied using the functional renormalization group, and close with an overview of the results obtained so far, as well as open questions.

Gradient flow on the lattice

• Antonio Rago

Room: 28B 110 t.b.a.

Causal Dynamical Triangulations. From the infrared to the ultraviolet.

• Jakub Gizbert-Studnicki (Jagiellonian University)

Room: 28B 110 One of key questions of quantum gravity is whether it can be formulated as a non-perturbatively renormalizable quantum field theory valid up to arbitrarily large energy scale as predicted by the, so-called, asymptotic safety conjecture. Causal Dynamical Triangulations (CDT) is a lattice quantum field theory of gravity based on the formalism of Regge Calculus and Feynman path integrals. It is studied by numerical Monte Carlo simulations. In my talk I will briefly introduce the four-dimensional CDT and present its most important results, including the non-trivial phase structure and the dynamically emerging semiclassical universe. I will discuss how one can define the infrared and ultraviolet limits of CDT and thus provide evidence in favour of asymptotic safety.

EDT as a tool to explore asymptotic safety

• Marc Schiffer (Radboud University)

Room: 28B 110 I will introduce EDT as a tool suitable to explore asymptotic safety on the lattice. In particular, I will show recent results that, if a non-trivial measure term is included, EDT might feature a physical phase, and a continuum limit.

The perturbative gradient flow

• Robert Harlander (RWTH Aachen University)

Room: 28B 110 I will give an introduction to the perturbative approach to the gradient flow in QCD and other field theories. The short-flow-time expansion will be discussed, and technical aspects for the calculation of the perturbative matching coefficients will be outlined. I will also present a number of examples, highlighting the benefits of the gradient flow in the calculation of physical observables.

The perturbative Ricci flow

• Henry Werthenbach (RWTH Aachen University)

Room: 28B 110 One candidate for a quantum theory of gravity is the Asymptotic Safety conjecture, which postulates the existence of a non-trivial fixed point for the gravitational couplings. We investigate the search for such a fixed point within the framework of perturbation theory. For this, we employ the Ricci flow as the central tool, pursuing a perturbative scheme analogous to the gradient flow formalism in QCD. In QCD, the gradient flow was introduced to bridge the gap between lattice simulations and perturbative calculations, allowing for a definition of a renormalization scheme that is accessible in both settings. Applied to gravity, the gradient flow is known as Ricci flow. In this talk, I will describe the perturbative implementation of the Ricci flow: the flow equation for the graviton field and its gauge fixing, the resulting Feynman rules, the BRST symmetry of the flowed theory, and its renormalization. On this basis we define Newton's coupling in the Ricci flow scheme and investigate its renormalization group behavior.

Gradient flow: applications not only to lattice QCD

• Piotr Korcyl (Jagiellonian University)

Room: 28B 110 Gradient flow equations provide continuous deformations of fields (gauge potentials, metrics, neural weights, etc.). They have been extensively studied and used in classical gravity, where they have allowed solving important problems. They are also employed routinely in lattice QCD calculations as a tool to define the strong coupling constant and thus to set the physical scale of simulations. The gradient descent algorithm used to train neural networks is yet another version of the same gradient flow equation. In the talk, I will introduce the gradient flow and describe its advantages and relationships in various contexts.

A Preliminary Approach to Ricci Flow in Dynamical Triangulations

• Andrzej Görlich (Jagiellonian University)

Room: 28B 110 I will present a preliminary approach to Ricci flow in the framework of Dynamical Triangulations. In particular, I will describe how to compute the geometric quantities required for evaluating the Regge action, including triangle areas, dihedral angles, and simplex volume, in a form suitable for numerical simulations. I will then discuss how to obtain the variations of these quantities with respect to the edge lengths. Finally, I will introduce and analyze the Ricci flow in the simple case of a single simplex.