Related papers: Product Integrals and Wilson loops

We give a gauge-independent definition of magnetic monopoles in the $SU(N)$ Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for…

We derive the Abelian - like expression for the lattice SU(N) Wilson loop in arbitrary irreducible representation. The continuum Abelian representation of the SU(N) Wilson loop (for the loop without selfintersections) that has been obtained…

In this short review main issues related to the non-Abelian Stokes theorem have been addressed. The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral…

Open Wilson lines are known to be the observables of noncommutative gauge theory with Moyal-Weyl star product. We generalize these objects to more general star products. As an application we derive a formula for the inverse Seiberg-Witten…

We consider the unparticle action that is made gauge invariant by inclusion of an open Wilson line factor. In deriving vertexes from such an action it has been customary to use a form of differentiating the Wilson line originally proposed…

We derive a version of non-Abelian Stokes theorem for SU(2) gauge fields in which neither additional integration nor surface ordering are required. The path ordering is eliminated by introducing the instantaneous color orientation of the…

We present results for Wilson loops in strongly coupled gauge theories. The loops may be taken around an arbitrarily shaped contour and in any field theory with a dual IIB geometry of the form M x S^5. No assumptions about supersymmetry are…

When G is a product of orthogonal, unitary and symplectic groups, we show that the Wilson loops generate a dense subalgebra of continuous observables on the configuration space of lattice gauge theory with structure group G.

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…

We discuss the derivation of the path integral representation over gauge degrees of freedom for Wilson loops in SU(N) gauge theory and 4-dimensional Euclidean space-time by using well-known properties of group characters. A discretized form…

We show that the unparticle action that is made gauge invariant by the inclusion of an open Wilson line factor can be transformed into the integral-differential operator action that avoids the use of the Wilson line factor. The two forms of…

We recall the non-Abelian Stokes theorem for the Wilson loop in the Yang-Mills theory and discuss its meaning. Then we move to `gravitational Wilson loops', i.e. to holonomies in curved d=2,3,4 spaces and derive non-Abelian Stokes theorems…

We reconsider the perturbative expansion of the Wilson loop in 2d noncommutative gauge theories, using an improved integration method. For the class of maximally crossed diagrams in the $\theta \to \infty$ limit we find an intriguing…

We provide a recursive diagrammatic prescription for the exponentiation of gauge theory amplitudes involving products of Wilson lines and loops. This construction generalizes the concept of webs, originally developed for eikonal form…

It is proposed an integral formulation of classical Yang-Mills equations in the presence of sources, based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. The formulation leads…

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 consider polygonal Wilson loops with null edges in conformal gauge theories. We derive an OPE-like expansion when several successive lines of the polygon are becoming aligned. The limit corresponds to a collinear, or multicollinear,…

We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for…

We discuss the divergence structure of Wilson line operators with partially overlapping segments on the basis of the cyclic Wilson loop as an explicit example. The generalized exponentiation theorem is used to show the exponentiation and…

Higher order terms in the effective action of noncommutative gauge theories exhibit generalizations of the *-product (e.g. *' and *-3). These terms do not manifestly respect the noncommutative gauge invariance of the tree level action. In…