Related papers: Physical Scaling and Renormalization Group in Two-…
In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
The renormalization of higher-dimensional operators in quantum field theory is essential for phenomenological analyses in particle physics, and plays a significant role in the study of critical phenomena. We present a framework for…
We recalculate the beta functions of higher derivative gravity in four dimensions using the one--loop approximation to an Exact Renormalization Group Equation. We reproduce the beta functions of the dimensionless couplings that were known…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
We consider the leading order perturbative renormalization of the multicritical $\phi^{2n}$ models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $\frac{1}{2}\xi…
We study the functional renormalization group equation and its solutions of the gravity having the background matters. From the system equivalence eliminating vacuum divergence, we are confirmed to give Newton coupling. We also give the…
We study the one loop renormalization in the most general metric-dilaton theory with the second derivative terms only. The general theory can be divided into two classes, models of one are equivalent to conformally coupled with gravity…
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…
Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
The renormalization structure of two-dimensional quantum gravity is investigated, in a covariant gauge. One-loop divergences of the effective action are calculated. All the surface divergent terms are taken into account, thus completing…
The renormalization group in effective quantum gravity can be consistently formulated using the Vilkovisky and DeWitt version of effective action and assuming a non-zero cosmological constant. Taking into account that the vacuum counterpart…
A new way how to calculate the off-shell renormalization functions within the $R^2$-gravity has been proposed. The one-loop renormalization group equations in the approach suggested have been constructed. The behaviour of effective…
Two-loop renormalization group equations in the standard model are re-calculated. A new coefficient is found in the beta-function of the quartic coupling and a class of gauge invariants are found to be absent in the beta-functions of…
Renormalization group equations play a central role in effective field theories, both maintaining perturbative control and allowing one to determine the correct low-energy phenomenology. In this work, we complete the one-loop…
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various…
Using as an example the Einstein gravity with the cosmological constant, we discuss the calculation of renormalization group functions off shell. We found, that gauge dependent terms should be absorbed by the nonlinear renormalization of…
The coefficient of the dimensionally regularized two-loop R^3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when non-dynamical three forms are added to the theory, or when a pseudo-scalar is replaced…