Related papers: Discovering and quantifying nontrivial fixed point…
The global structure of the renormalization-group flows of a model with isotropic and cubic interactions is studied using the massive field theory directly in three dimensions. The four-loop expansions of the $\bt$-functions are calculated…
We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may…
We apply the non-perturbative renormalization group method to a class of out-of-equilibrium phase transitions (usually called ``parity conserving'' or, more properly, ``generalized voter'' class) which is out of the reach of perturbative…
In (2+1) dimensions, we consider the model of a $N$ flavor, two-component fermionic field interacting through a Chern-Simons field besides a four fermion self-interaction which consists of a linear combination of the Gross-Neveu and…
We study an ${\cal N} = 2$ supersymmetric generalization of the three-dimensional critical $O(N)$ vector model that is described by $N+1$ chiral superfields with superpotential $W = g_1 X \sum_i Z_i^2 + g_2 X^3$. By combining the tools of…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasi-statically changing the applied source at…
We study the multicritical behavior arising from the competition of two distinct types of ordering characterized by O(n) symmetries. For this purpose, we consider the renormalization-group flow for the most general $O(n_1)\oplus…
Asymptotically safe extensions of the Standard Model have been searched for by adding vector-like fermions charged under the Standard Model gauge group and having Yukawa-like interactions with new scalar fields. Here we study the…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
We systematically explore the space of renormalization group flows of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant…
We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…
We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points for $O(N)$-symmetric models with quenched disorder in two dimensions. Random fixed points are characterized by two disorder…
We review the asymptotic safety scenario for quantum gravity and the role and implications of an underlying ultraviolet fixed point. We discuss renormalisation group techniques employed in the fixed point search, analyse the main picture at…
I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite…
We construct supersymmetric conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use the Wilsonian renormalization group equation method, which is one of the…
I review recent work on the infrared structure of (2+1)-dimensional Abelian gauge theories and their application to condensed matter physics. In particular, within a large-N Schwinger-Dyson treatment, and including an `infrared momentum…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…