Related papers: An Extension of Pohlmeyer's Theorem
In 2+1 dimensions, we propose a renormalizable non-linear sigma model action which describes the $\mathcal{N}=2$ supersymmetric generalization of Galilean Electrodynamics. We first start with the simplest model obtained by null reduction of…
The field theoretic renormalization group is applied to Kraichnan's model of a passive scalar quantity advected by the Gaussian velocity field with the pair correlation function $\propto\delta(t-t')/k^{d+\epsilon}$. Inertial-range anomalous…
Numerous topics in three and four dimensional supersymmetric gauge theories are covered. The organizing principle in this presentation is scaling (Wilsonian renormalization group flow.) A brief introduction to scaling and to supersymmetric…
We propose a simple fixed point scenario in the renormalization flow of a scalar dilaton coupled to gravity. This would render gravity non-perturbatively renormalizable and thus constitute a viable theory of quantum gravity. On the fixed…
We use lattice simulations and the continuous renormalization-group method, based on the gradient flow, to calculate the $\beta$ function and anomalous dimensions of the SU(3) gauge theory with $N_f=10$ flavors of fermions in the…
We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase…
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
The holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed. The geometrical constraints on the target space of the 4d, N=2 non-linear sigma-models in…
We propose a continuous real space renormalization group transformation based on gradient flow, allowing for a numerical study of renormalization without the need for costly ensemble matching. We apply our technique in a pilot study of…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
We use the functional renormalization group and the $\epsilon$-expansion concertedly to explore multicritical universality classes for coupled $\bigoplus_i O(N_i)$ vector-field models in three Euclidean dimensions. Exploiting the…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
In the framework of the renormalization-group theory of critical phenomena, a quantitative description of many continuous phase transitions can be obtained by considering an effective $\Phi^4$ theories, having an N-component fundamental…
We consider a simple but generic model of gravity where Weyl--invariance is realized thanks to the presence of a gauge field for dilatations. We quantize the theory by suitably defining renormalization group flows that describe the…
We analyse the renormalisation group flow of quantum gravity at sixth order in the derivative expansion within the background field approximation. Non-linear field redefinitions are used to ensure that only essential couplings flow. Working…
We show that renormalized non-commutative scalar field theories do not reduce to their planar sector in the limit of large non-commutativity. This follows from the fact that the RG equation of the Wilson-Polchinski type which describes the…
Anomaly, a generic feature of relativistic quantum field theory, is shown to be present in non-relativistic classical ideal fluid. A new result is the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms…
We complete our study of non-Abelian gauge theories in the framework of Epstein-Glaser approach to renormalization theory including in the model an arbitrary number of Dirac Fermions. We consider the consistency of the model up to the third…
The consistent form of the gauge anomaly is worked out at first order in $\theta$ for the noncommutative three-point function of the ordinary gauge field of certain noncommutative chiral gauge theories defined by means of the Seiberg-Witten…
The dilation invariance is studied in the framework of Epstein-Glaser approach to renormalization theory. Some analogues of the Callan-Symanzik equations are found and they are applied to the scalar field theory and to Yang-Mills models. We…