Related papers: The geometric $\beta$-function in curved space-tim…
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…
Renormalisation Group (RG) flows in theory space (the space of couplings) are generated by a vector field -- the $\beta$ function. Using a specific metric ansatz in theory space and certain methods employed largely in the context of General…
In this paper, I show a close connection between renormalization and a generalization of the Dynkin operator in terms of logarithmic derivations. The geometric $\beta$ function, which describes the dependence of a Quantum Field Theory on an…
The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the…
We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
The renormalization group flow equation obtained by means of a proper time regulator is used to calculate the two loop beta function and anomalous dimension eta of the field for the O(N) symmetric scalar theory. The standard perturbative…
Random noncommutative geometry can be seen as a Euclidean path-integral approach to the quantization of the theory defined by the Spectral Action in noncommutative geometry (NCG). With the aim of investigating phase transitions in random…
A global connection on the Connes Marcolli renormalization bundle relates $\beta$-functions of a class of regularization schemes by gauge transformations, as well as local solutions to $\beta$-functions over curved space-time.
We explore a geometric perspective on quantum field theory by considering the configuration space, where all field configurations reside. Employing $n$-particle irreducible effective actions constructed via Legendre transforms of the…
Renormalization schemes and cutoff schemes allow for the introduction of various distinct renormalization scales for distinct couplings. We consider the coupled renormalization group flow of several marginal couplings which depend on just…
In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function…
We apply the functional renormalization group approach to a $\mathcal{N}=1$ supersymmetric gauge model with one chiral superfield coupled to a vector $U(1)$ superfield. We find that the nonrenormalization theorem still works at leading…
The renormalization group flow in two-dimensional field theories that are coupled to gravity has unusual features: First, the flow equations are second order in derivatives. Second, in the presence of handles the flow has quantum mechanical…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…
The behavior of the beta-function of the low-energy effective coupling in the N=2 supersymmetric SU(2) QCD with several massive matter hypermultiplets and in the SU(3) Yang-Mills theory is determined near the superconformal points in the…
In this work, we present a holographic renormalization scheme for asymptotically anti-de Sitter spacetimes in which the dual renormalization scheme of the boundary field theory is dimensional regularization. This constitutes a new level of…
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…
We derive and solve flow equations for a general O(N)-symmetric effective potential including wavefunction renormalization corrections combined with a heat-kernel regularization. We investigate the model at finite temperature and study the…
It is shown that the renormalisation group (RG) equation can be viewed as an equation for Lie transport of physical amplitudes along the integral curves generated by the $\beta$-functions of a quantum field theory. The anomalous dimensions…