Related papers: Gradient flows for $\beta$ functions via multi-sca…
We construct exact functional renormalization group (RG) flow equations for non-relativistic fermions in arbitrary dimensions, taking into account not only mode elimination but also the rescaling of the momenta, frequencies and the…
First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG…
We review recent developments in the theory of renormalisation group flows in minimal models with boundaries. Among these, we discuss in particular the perturbative calculations of Recknagel et al, not only as a tool to predict the IR…
Renormalization group equations are derived for the case when both valley splitting and intervalley scattering are present in a two-valley system. A third scaling parameter is shown to be relevant when the two bands are split but otherwise…
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d…
We calculate the step scaling function, the lattice analog of the renormalization group $\beta$-function, for an SU(3) gauge theory with twelve flavors. The gauge coupling of this system runs very slowly, which is reflected in a small step…
We focus on functional renormalization for ensembles of several (say $n\geq 1$) random matrices, whose potentials include multi-traces, to wit, the probability measure contains factors of the form $ \exp[-\mathrm{Tr}(V_1)\times\ldots\times…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
In this talk the methods and computer tools which were used in our recent calculation of the three-loop Standard Model renormalization group coefficients are discussed. A brief review of the techniques based on special features of…
Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…
Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing…
This PhD thesis is devoted to show that differential renormalization is a simple and useful renormalization method that we can use when dealing with gauge theories. In this work, it is shown how the one-loop results of Constraint…
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…
We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the…
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.
The flow equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one dimensional model with power-law decaying hoppings. This model presents a…
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…
It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for…