Related papers: The Functional Renormalization Group in Quantum Gr…
We explore the nonperturbative renormalization group flow of Quantum Einstein Gravity (QEG) on an infinite dimensional theory space. We consider "conformally reduced" gravity where only fluctuations of the conformal factor are quantized and…
The renormalization group flow of unimodular quantum gravity is investigated within two different classes of truncations of the flowing effective action. In particular, we search for non-trivial fixed-point solutions for polynomial…
We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein K\"{a}hler manifolds are aymptotically free. This…
Application of asymptotic freedom to the ultraviolet stability in Euclidean quantum field theories is revisited and illustrated through the hierarchical model making also use of a few technical developments that followed the original works…
Starting from an ultraviolet fixed point, we study the infrared behavior of quantum Weyl gravity in terms of a functional renormalization group (RG) flow equation. To do so, we employ two classes of Bach-flat backgrounds, namely maximally…
The perturbative renormalization group(RG) equation is applied to resum divergent series of perturbative wave functions of quantum anharmonic oscillator. It is found that the resummed series gives the cumulant of the naive perturbation…
We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $\beta$-functions for all…
In this chapter we review the state-of-the-art of black holes in asymptotically safe gravity. After a brief recap of the asymptotic safety program, we shall summarize the features of asymptotic-safety-inspired black-hole models that have…
We derive an exact functional renormalization group equation for the projectable version of Ho\v{r}ava-Lifshitz gravity. The flow equation encodes the gravitational degrees of freedom in terms of the lapse function, shift vector and spatial…
We investigate finite lattice approximations to the Wilson Renormalization Group in models of unconstrained spins. We discuss first the properties of the Renormalization Group Transformation (RGT) that control the accuracy of this type of…
An introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics is presented in the form of 6 lectures delivered to the British Universities Summer School in Theoretical…
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…
The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes…
We describe a new formulation of the functional renormalization group (RG) for interacting fermions within a Wilsonian momentum-shell approach. We show that the Luttinger-Ward functional is a fixed point of the RG, and derive the infinite…
This article presents a tutorial introduction to a recently developed real-time renormalization group method. It describes nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We illustrate the technique…
We construct a special-purpose functional flow equation which facilitates non-perturbative renormalization group (RG) studies on theory spaces involving a large number of independent field components that are prohibitively complicated using…
The effective action in quantum general relativity is strongly dependent on the gauge-fixing and parametrization of the quantum metric. As a consequence, in the effective approach to quantum gravity, there is no possibility to introduce the…
Asymptotic Safety is a promising framework towards the understanding, in a non-perturbative way, of Quantum Gravity. It treats the Newton's constant G_N and the cosmological constant \Lambda as running coupling of an effective action. At…
We briefly review the previous works on the renormalization group in quantum general relativity with the cosmological constant, based on the Vilkovisky and DeWitt version of effective action. On top of that, we discuss the prospects of the…
Physics in the vicinity of an ultraviolet stable fixed point of a quantum field theory is parametrized by a renormalization group invariant macroscopic length scale, the correlation length $\xi,$ with the quantum effective action a function…