Related papers: Real valued functions for BFKL eigenvalue
Two gauge and diffeomorphism invariant theories on the Yang-Mills phase space are studied. They are based on the Lie-algebras $so(1,3)$ and $\widetilde{so(3)}$ -- the loop-algebra of $so(3)$. Although the theories are manifestly real, they…
We work out the map between null polygonal hexagonal Wilson loops and spinning three point functions in large $N$ conformal gauge theories by mapping the variables describing the two different physical quantities and by working out the…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
A broad class of observables in four-dimensional $\mathcal{N}=2$ and $\mathcal{N}=4$ superconformal Yang-Mills theories can be exactly computed for arbitrary 't Hooft coupling as Fredholm determinants of integrable Bessel operators. These…
The multi-Regge limit of scattering amplitudes in strongly-coupled $\mathcal{N}=4$ super Yang-Mills is described by the large mass limit of a set of thermodynamic Bethe ansatz (TBA) equations. A non-trivial remainder function arises in this…
We consider a three-dimensional effective theory of Polyakov lines derived previously from lattice Yang-Mills theory and QCD by means of a resummed strong coupling expansion. The effective theory is useful for investigations of the phase…
Let $h(B_d)$ denote the space of real-valued harmonic functions on the unit ball $B_d$ of $\mathbb{R}^d$, $d\ge 2$. Given a radial weight $w$ on $B_d$, consider the following problem: construct a finite family $\{f_1, f_2, \dots, f_J\}$ in…
This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex…
Two-dimensional supergravity theory is quantized as an anomalous gauge theory. In the Batalin-Fradkin (BF) formalism, the anomaly-canceling super-Liouville fields are introduced to identify the original second-class constrained system with…
First we establish a weighted Reilly formula for differential forms on a smooth compact oriented Riemannian manifold with boundary. Then we give two applications of this formula when the manifold satisfies certain geometric conditions. One…
This paper first reviews how anti-symmetric matrices in two dimensions yield imaginary eigenvalues and complex eigenvectors. It is shown how this carries on to rotations by means of the Cayley transformation. Then a real geometric…
We give a complete, self-contained, and mathematically rigorous proof that Euclidean Yang-Mills theories are perturbatively renormalisable, in the sense that all correlation functions of arbitrary composite local operators fulfil suitable…
The integrals defining the two-loop beta-function for the general renormalizable N=1 supersymmetric Yang--Mills theory, regularized by higher covariant derivatives, are investigated. It is shown that they are given by integrals of double…
We present the results of two-loop calculations of the anomalous dimension matrix for the Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory for polarized and unpolarized cases. This matrix can be transformed to a triangle…
In this paper we recover the non-perturbative partition function of 2D~Yang-Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D~Yang-Mills theory on surfaces…
We introduce first weighted function spaces on Rd using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on…
We show that dual conformal symmetry, mainly studied in planar $\mathcal N = 4$ super-Yang-Mills theory, has interesting consequences for Feynman integrals in nonsupersymmetric theories such as QCD, including the nonplanar sector. A simple…
As a first step towards a strong coupling expansion of Yang-Mills theory, the SU(2) Yang-Mills quantum mechanics of spatially constant gauge fields is investigated in the symmetric gauge, with the six physical fields represented in terms of…
Topological gravity is equivalent to physical gravity in two dimensions in a way that is still mysterious, though by now it has been proved by Kontsevich. In this paper it is shown that a similar relation between topological and physical…
A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the…