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The ambiguities inherent in renormalization are considered when using mass-independent renormalization in massless theories that involve two coupling coupling constants. We review how there is no renormalization scheme in which the…
The use of entanglement renormalization in the presence of scale invariance is investigated. We explain how to compute an accurate approximation of the critical ground state of a lattice model, and how to evaluate local observables,…
Drawing on analogies with the commutative case, the Wilsonian picture of renormalization is developed for noncommutative scalar field theory. The dimensionful noncommutativity parameter, theta, induces several new features. Fixed-points are…
Two-loop $\beta$-function and anomalous dimension are calculated for N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives in the minimal subtraction scheme. The result for two-loop contribution to the…
In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…
It is shown that exact renormalization group (RG) equations (including rescaling and field-renormalization) for respectively the scale-dependent full action $S[\phi,t]$ and the scale-dependent full effective action $\Gamma[\Phi,t]$ --in…
We compute the running of the mass of a neutral boson and of its self-coupling in a simple model describing the self-interaction of three scalars, one of them neutral and the other two electrically charged, subject to the effects of a…
For various two dimensional non linear $\sigma$ models, we present a direct comparison between the $\beta$ functions computed with the $2+\epsilon$ renormalization group and the $\beta$ functions measured by Monte Carlo simulations. The…
We examine a class of gauge theories obtained by projecting out certain fields from an N=4 supersymmetric SU(N) gauge theory. These theories are non-supersymmetric and in the large N limit are known to be conformal. Recently it was proposed…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
A Lorentz and gauge symmetry preserving regularization method is proposed in 4 dimension based on momentum cutoff. We use the conditions of gauge invariance or freedom of shift of the loop-momentum to define the evaluation of the terms…
Three-loop $\beta$-functions of the Minimal Supersymmetric Standard Model regularized by higher covariant derivatives are obtained for an arbitrary supersymmetric subtraction scheme. For this purpose we first calculate two-loop anomalous…
Using a simple solvable model, i.e., Higgs--Yukawa system with an infinite number of flavors, we explicitly demonstrate how a dimensional continuation of the $\beta$ function in two dimensional MS scheme {\it fails\/} to reproduce the…
We discuss the arbitrariness in the choice of cutoff scheme in calculations of beta functions. We define a class of "pure" cutoff schemes, in which the cutoff is completely independent of the parameters that appear in the action. In a sense…
In this note we show that $\beta'_*$, the $\beta$-function slopes in the electric and magnetic theories are equal at the corresponding infrared fixed points. This follows from the scaling of the correlators of the trace of the energy…
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar $\phi$ with…
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 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…
We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an…
The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the…