Related papers: Running Coupling Constants in 2D Gravity
The renormalization group method in $R^2$-gravity without matter fields is discussed. A criterion for the existence of the renormalization constant for the metric has been found, two-loop higher order poles have been calculated, a relation…
We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge…
A modified gravitational theory is developed in which the gravitational coupling constants $G$ and $Q$ and the effective mass $m_\phi$ of a repulsive vector field run with momentum scale $k$ or length scale $\ell =1/k$, according to a…
We discuss the relationship between geometry, the renormalization group (RG) and gravity. We begin by reviewing our recent work on crossover problems in field theory. By crossover we mean the interpolation between different representations…
We consider the dipole-dipole correlations for the two-dimensional Coulomb gas/sine-Gordon model for $\beta> 8\pi$ by a renormalization group method. First we re-establish the renormalization group analysis for the partition function using…
We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable, but not conformal invariant. Questions concerning the $\b$ function and the effective action are addressed, and the effective action and the…
The renormalisation group (RG) flow on the space of couplings of a simple model with two couplings is examined. The model considered is that of a single component scalar field with $\phi^4$ self interaction coupled, via Yukawa coupling, to…
We consider a bosonic $\s$--model coupled to two--dimensional gravity. In the semiclassical limit, $c\rightarrow -\infty$, we compute the gravity dressing of the $\b$--functions at two--loop order in the matter fields. We find that the…
Higher order renormalization in 4D quantum gravity is carried out using dimensional regularization with great care concerning the conformal-mode dependence. In this regularization, resummation can be automatically carried out without making…
We show that one can use some renormalized coupling constants to compute the free energy and correlation functions at all critical points of the two-dimensional topological gravity in a uniform way. In particular, one can derive the…
We show that if the beta functions of a field theory are given by the gradient of a certain potential on the space of couplings, a gravitational background in one more dimension can express the renormalization group (RG) flow of the theory.…
Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d >= 3 of dimensions by means of Wegner's and Houghton's, and by way of the real-space RG approaches. The…
The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar…
A family of connections on the space of couplings for a renormalizable field theory is defined. The connections are obtained from a Levi-Civita connection, for a metric which is a generalisation of the Zamolodchikov metric in two…
Flows of the couplings of a theory of an N-component (complex) scalar field coupled to electrodynamics is investigated using the functional renormalization group formalism in d dimensions in covariant gauges. We find charged fixed points…
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 discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…
Matrix models of 2d quantum gravity coupled to matter field are investigated by the renormalized perturbational method, in which the matrix model Hamiltonian is represented by the equivalent vector model. By the saddle point method, the…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…