Related papers: Exponentiation for products of Wilson lines within…
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
It is well known that a Wilson action reduces to the generating functional of connected correlation functions as we take the momentum cutoff to zero. For a fixed point Wilson action, this implies that for momenta large compared with the…
We investigate Schwinger-Dyson equations for correlators of Wilson line operators in non-commutative gauge theories. We point out that, unlike what happens for closed Wilson loops, the joining term survives in the planar equations. This…
Many widely used network centralities are based on counting walks that meet specific criteria. This paper introduces a systematic framework for walk enumeration using generating functions. We introduce a first-passage decomposition that…
An effective action is proposed to compute the expectation value of Wilson loops in $(S)U(N)$ gauge theories. The action consists of fermions localized on the loop and an Abelian gauge field that fixes the representation. The discussion is…
We study the large $N$ expansion of winding Wilson loops in the off-critical regime of the Gross-Witten-Wadia (GWW) unitary matrix model. These have been recently considered in arXiv:1705.06542 and computed by numerical methods. We present…
We shall interpret the null hexagonal Wilson loop (or, equivalently, six gluon scattering amplitude) in 4D ${\cal N}=4$ Super Yang-Mills, or, precisely, an integral representation of its matrix part, via an ADHM-like instanton construction.…
We derive an evolution equation for the generating functional which accounts for processes for both gluon emission and recombination. In terms of color dipoles, the kernel of this equation describes evolution as a classical branching…
We present an explicit formula for the expected value of a product of several independent symplectically invariant matrices in which the trace and real part function may be applied, possibly to different subexpressions. This takes the form…
This study introduces a procedure to obtain general expressions, $y = f(x)$, subject to linear constraints on the function and its derivatives defined at specified values. These constrained expressions can be used describe functions with…
For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size $N$, in term of a determinant; this determinant is…
In this paper, we introduce a new four-parameter generalization of the exponentiated Weibull (EW) distribution, called the exponentiated Weibull-logarithmic (EWL) distribution, which obtained by compounding EW and logarithmic distributions.…
The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…
In this paper we propose a semi-empirical modeling framework for aggregated electrical load and generation using an equivalent circuit formulation. The proposed models are based on complex rectangular voltage and current state variables…
Wilson's approximation scheme of RG recursion formula dropping momentum dependence of the propagators is applied to large-$N$ vector and matrix models in dimensions $2<d<4$ by making use of their exact solutions in zero dimension. In spite…
Recently, the concept of generating function has been employed in one-loop reduction. For one-loop integrals encompassing arbitrary tensor ranks and higher-pole contributions, the generating function can be decomposed into a tensor part and…
Wilson loop diagrams are an important tool in studying scattering amplitudes of SYM $N=4$ theory and are known by previous work to be associated to positroids. In this paper we study the structure of the associated positroids, as well as…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-$k$ symmetric representation of the gauge group $U(N)$ for ${\cal N} = 4$ super Yang-Mills. We find the holographic…
This short note studies the asymptotic behavior of a generating function associated with the decimal expansion of \(2^n\). Our aims are twofold: (i) to present a problem on the best possible upper bound for this behavior, and (ii) to…