Related papers: Integrability and Wilson loops: the wavy line cont…
We study the correlator of two parallel Wilson lines in two-dimensional noncommutative Yang-Mills theory, following two different approaches. We first consider a perturbative expansion in the large-N limit and resum all planar diagrams. The…
The derivation of the explicit formula for the vacuum expectation value of the Wilson loop functional for an arbitrary gauge group on an arbitrary orientable two-dimensional manifold is considered both in the continuum case and on the…
We study the controllability of linearized shape-dependent operators for flow problems. The first operator is a mapping from the shape of the computational domain to the tangential wall velocity of the potential flow problem and the second…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Null Polygon Wilson Loops (WL) in N=4 SYM can be computed using the Operator Product Expansion in terms of a transition amplitude on top of a color flux tube (FT). That picture is valid at any value of the 't Hooft coupling. So far it has…
We discuss how to implement, in lattice gauge theories, external charges which are not commensurate with an elementary gauge coupling. It is shown that an arbitrary, real power of a standard Wilson loop (or Polyakov line) can be defined and…
This short note is some obvious mathematical addendum to our papers on Wilson loops on polygon-like contours with circular edges \cite{Dorn:2020meb,Dorn:2020vzj}. Using the technique of osculating spheres and circles we identify the…
In the context of integrated correlators in $\mathcal{N}=4$ SYM, we study the 2-point functions of local operators with a superconformal line defect. Starting from the mass-deformed $\mathcal{N}=2^*$ theory in presence of a…
A recently proposed connection between closed string field and an open Wilson line defined on an arbitrary contour is further explored here. We suggest that reparametrization invariance of a Wilson line is the principle which determines the…
Wilson loop expectations at weak coupling are computed to first order, for four dimensional lattice gauge theories with finite gauge groups which satisfy some mild additional conditions. This continues recent work of Chatterjee, which…
The Dyson equation proposed for planar temporal Wilson loops in the context of supersymmetric gauge theories is critically analysed thereby exhibiting its ingredients and approximations involved. We reveal its limitations and identify its…
Linear spin wave theory provides the leading term in the calculation of the excitation spectra of long-range ordered magnetic systems as a function of $1/\sqrt{S}$. This term is acquired using the Holstein-Primakoff approximation of the…
We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic vibration. The analysis is performed…
In this paper we study string theory in the background $\mathcal{M}_3$ that interpolates between $AdS_3$ in the IR and linear dilaton spacetime $\mathbb{R}^{1,1}\times\mathbb{R}_\phi$ in the UV. Via holographic duality this background…
We compute correlation functions of protected primaries on the $1/2$-BPS Wilson loop in ${\cal N}$ = 4 super Yang-Mills theory at weak coupling. We first perform direct perturbative computation at one loop in the planar limit and present…
In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and $R$-matrix of the two-loop SU(2) sector in…
We examine the manner in which a linear potential results from fluctuations due to vortices linked with the Wilson loop. Our discussion is based on exact relations and inequalities between the Wilson loop and the vortex and electric flux…
For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…
We give the formula for a simple Wilson loop on a sphere which is valid for an arbitrary QCD$_2$ saddle-point $\rho(x)$: \mbox{$W(A_1,A_2)=\oint \frac{dx}{2\pi i} \exp(\int dy \frac{\rho(y)}{y-x}+A_2x)$}. The strong-coupling-phase solution…
We calculate quark-antiquark potentials using the relationship between the expectation value of the Wilson loop and the action of a probe string in the string dual. We review and categorize the possible forms of the dependence of the energy…