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We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the renormalization group is treated as a scalar field at the level of the action and determined in…
By formulating the renormalization group as a quantum channel acting on density matrices in Quantum Field Theories (QFTs), we show that ground-state expectation values of observables supported on slow momentum modes can be approximated by…
We derive several results concerning non-perturbative renormalization in the spherical field formalism. Using a small set of local counterterms, we are able to remove all ultraviolet divergences in a manner such that the renormalized theory…
Perturbation theory, as well as most thermal field resummation methods widely used to study finite-temperature quantum field theories, presents a non-negligible renormalization scale dependence. To address this limitation, we propose an…
This is a self-contained purely algebraic treatment of desingularization of fields of fractions $\mathbf{L}:=Q(\mathbf{A})$ of $d$-dimensional domains of the form \[\mathbf{A}:=\bar{\mathbf{F}}[\underline{x}]/\langle…
Invariance of the effective action under changes of the renormalization scale $\mu$ leads to relations between those (presumably calculated) terms independent of $\mu$ at a given order of perturbation theory and those higher order terms…
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 differential equations of the Wilson renormalization group are a powerful tool to study the Schwinger functions of Euclidean quantum field theory. In particular renormalization theory can be based entirely on inductively bounding their…
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation,…
We obtain the renormalization group(RG) functions for the massless scalar field theory where symmetry breaking occurs radiatively. After obtaining the effective potential for the radiative symmetry breaking scheme from that of the minimal…
Standard zeta function regularisation enforces a scale-independent prescription for spectral aggregation, effectively fixing the relative weight of spectral contributions. We relax this constraint by replacing the derivative at $s=0$ with a…
Scalar field theories with $\mathbb{Z}_{2}$-symmetry are the traditional playground of critical phenomena. In this work these models are studied using functional renormalization group (FRG) equations at order $\partial^2$ of the derivative…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
The Caswell-Wilczek analysis on the gauge dependence of the effective action and the renormalization group functions in Yang-Mills theories is generalized to generic, possibly power counting non renormalizable gauge theories. It is shown…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
We study the regularization ambiguities in an exact renormalized (1+1)-dimensional field theory. We show a relation between the regularization ambiguities and the coupling parameters of the theory as well as their role in the implementation…
We consider Lifshitz-type scalar theories with explicit breaking of the Lorentz symmetry that, in addition, exhibit anisotropic scaling laws near the ultraviolet fixed point. Using the proper time regularization method on the spatial…
We consider formulations of the functional renormaliztion-group flow for correlated electronic systems, having the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those…
For cosmologies including scale dependence of both the cosmological and the gravitational constant, an additional consistency condition dictated by the Bianchi identities emerges, even if the energy-momentum tensor of ordinary matter stays…