Related papers: Naturalness and Renormalization Group in the Stand…
A proper version of the proto renormalization-group scheme is presented to derive amplitude equations in striped pattern formation with conserved and nonconserved order parameter. In the conserved case, the result preserves the conservation…
Various formulations of the exact renormalization group can be compared in the perturbative domain, in which we have reliable expressions for regularization-independent (universal) quantities. We consider the renormalization of the…
It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded…
Models with a light, additional gauge boson are attractive extensions of the standard model. Often these models are only considered as effective low energy theory without any assumption about an UV completion. This leaves not only the…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
We discuss how the ordinary renormalization group (RG) equations arise in the context of Wilson's exact renormalization group (ERG) as formulated by Polchinski. We consider the phi4 theory in four dimensional euclidean space as an example,…
We consider the so-called $\natural$-model. It is an one-default model which gives the conditional law of a random time with respect to a reference filtration. This model has been studied in the case where the parameters are continuous. In…
It is a well-known empirical phenomenon that natural axiomatic theories are pre-well-ordered by consistency strength. Without a precise mathematical definition of "natural," it is unclear how to study this phenomenon mathematically. We will…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
Complex systems with many degrees of freedom are typically intractable, but some of their behaviors may admit simpler effective descriptions. The question of when such effective descriptions are possible remains open. The paradigmatic…
The notion of a natural model of type theory is defined in terms of that of a representable natural transfomation of presheaves. It is shown that such models agree exactly with the concept of a category with families in the sense of Dybjer,…
A common approach in physics and mathematics is to extend and modify theories and frameworks by considering what is often described as a `natural' extension or modification by including higher-order terms or by introducing other…
We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless…
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…
We provide an analysis of the structure of renormalisation scheme invariants for the case of $\phi^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants up to four loops and include some partial results at…
The scale hierarchy of wavelets provides a natural frame for renormalization. Expanding the order parameter of the Landau-Ginzburg/$\Phi^4$ model in a basis of compact orthonormal wavelets explicitly exhibits the coupling between scales…
$N$-naturalness is a novel solution to the electroweak hierarchy problem which posits $N$ copies of the Standard Model with varying Higgs mass-squared parameters. Reheating proceeds through a "reheaton" particle that deposits most of its…
We propose that the broad architecture of the renormalization group flow in quantum field theories is, at least in part, fixed by unitarity. The precise statement is summarized in the Unitarity Flow Conjecture, which states that the…