Related papers: Trace anomaly for 4D higher derivative scalar-dila…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
We review the derivation of the Liouville action in 2DQG via the trace anomaly and emphasize how a similar approach can be used to derive an effective action describing the long wavelength dynamics of the conformal factor in 4D. In 2D we…
The 1-loop anomalies of a d-dimensional quantum field theory can be computed by evaluating the trace of the regulated path integral jacobian matrix, as shown by Fujikawa. In 1983, Alvarez-Gaum\'e and Witten observed that one can simplify…
The curvature of a higher spin potential as constructed in a previous article of the same authors arXiv:0705.3528 is applied to the analysis of the linearized trace anomaly obtained from the quadratic part of the effective action for a…
We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of $6D$, ${\cal N}=(1,0)$ supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration…
We consider ${\cal N} =1$ supersymmetric gauge theories in the conformal window. The running of the gauge coupling is absorbed into the metric by applying a suitable matter superfield- and Weyl-transformation. The computation becomes…
We report on the computation of the effective actions describing the interaction of gravity both for an abelian and a non-abelian gauge theory, mediated by the trace anomaly.
Modern software systems have become increasingly complex, which makes them difficult to test and validate. Detecting software partial anomalies in complex systems at runtime can assist with handling unintended software behaviors, avoiding…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
Anomaly detection is the process of finding data points that deviate from a baseline. In a real-life setting, anomalies are usually unknown or extremely rare. Moreover, the detection must be accomplished in a timely manner or the risk of…
In the scalar $\phi^4$ field model the dispersive approach to the trace anomaly is proposed. It is shown that it is impossible to get dispersion representation for all formfactors so that preserve both the translation and dilatation Ward…
The reduction of 4d matter-gravity theory to $S_2$, $H_2$ or $R_2$ leads to effective 2d dilatonic gravity with dilaton coupled matter. Spinors give the exceptional example of the theory which is conformally invariant in 4d as well as in…
A new fourth partial derivative is introduced for the study of transport dynamics. It is a Lagrangian partial derivative following the path of diffusion, not the path of convection. Use of this derivative decouples the effect of diffusion…
The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference of which is trace-class and one of the two a strict…
Standard and anomalous transport in incompressible flow is investigated using multiscale techniques. Eddy-diffusivities emerge from the multiscale analysis through the solution of an auxiliary equation. From the latter it is derived an…
The purpose of this paper is to present the critical cases of the trace theorems for the restriction of functions to closed surfaces, and to give the asymptotics for the norms of the traces under dilations of the surface. We also discuss…
Explaining outliers occurrence and mechanism of their occurrence can be extremely important in a variety of domains. Malfunctions, frauds, threats, in addition to being correctly identified, oftentimes need a valid explanation in order to…
Any intelligent traffic monitoring system must be able to detect anomalies such as traffic accidents in real time. In this paper, we propose a Decision-Tree - enabled approach powered by Deep Learning for extracting anomalies from traffic…
The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…