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We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier…
We consider the Yang-Mills problem on $\mathbb{R}^{1+4}$ with gauge group $SO(4)$. In an appropriate equivariant reduction, this Yang-Mills problem reduces to a single scalar semilinear wave equation. This semilinear equation admits a…
Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions. The gluon mass is introduced by coupling the gauge field to an SU(N) principal chiral nonlinear sigma model. The proof of renormalizability relies on the asymptotic…
A necessary ingredient for our previous results on the form of the long distance effective action of the twisted lattice N=4 super Yang-Mills theory is the existence of a real space renormalization group which preserves the lattice…
We propose a gauge-invariant version of Wilson Renormalization Group for thermal field theories in real time. The application to the computation of the thermal masses of the gauge bosons in an SU(N) Yang-Mills theory is discussed.
We review recent progress in the understanding of symmetries for scattering amplitudes in N=4 superconformal Yang-Mills theory. It is summarized how the superficial breaking of superconformal symmetry by collinear anomalies and the…
We calculate the mass dependent renormalization factors of heavy-light bilinears at one-loop order of perturbation theory, when the heavy quark is treated with the Fermilab formalism. We present numerical results for the Wilson and…
We analyze a model of cold axion Dark Matter weakly coupled with a dark gluon condensate, reproducing Dark Energy. We first review how to recover the Dark Energy behavior using the functional renormalization group approach, and ground our…
We present a family of nonrelativistic Yang-Mills gauge theories in D+1 dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2. The ground state wavefunction is…
The aim of these lectures is to describe a construction, as self-contained as possible, of renormalized gauge theories. Following a suggestion of Polchinski, we base our analysis on the Wilson renormalization group method. After a…
Matrix model describing the anomalous dimensions of composite operators in $\mathcal{N}=4$ super Yang--Mills theory up to one-loop level is considered at finite temperature. We compute the thermal effective action for this model, which we…
It is shown, by explicit calculation in the axial gauge, that the renormalization group flow for the Wilson loop in perturbation theory does exhibit singularities and consequently it can not eventually reproduce the gauge invariant result,…
We use the Wilson renormalization group (RG) formulation to solve the fine-tuning procedure needed in renormalization schemes breaking the gauge symmetry. To illustrate this method we systematically compute the non-invariant couplings of…
Schr\"odinger equation with potential $-g/r^2$ exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r=0$. Instead, we use the renormalization group…
Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model in three and four dimensions, as well…
We analyze the slow roll limit of the massive version of time-dependent Yang--Mills type matrix model. We find that this limit reproduces the one-loop non-Hermitian matrix model, describing the dilatations of the local gauge invariant…
We employ an adaptation of a strong-disorder renormalization-group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse…
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions,…
We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent expansion about epsilon = 0 including the finite terms. The amplitude was constructed…
I discuss various situations in which perturbative expansions are used in Yang-Mills theories with asymptotic freedom and establish the limits of its applicability.