Related papers: Wilson surface observables from equivariant cohomo…
We study topological gauge theories with N=(2,0) supersymmetry based on stable bundles on general Kahler 3-folds. In order to have a theory that is well defined and well behaved, we consider a model based on an extension of the usual…
These notes provide an introduction toward Wilson loops in N=4 supersymmetric Yang-Mills theory with a focus toward their integrability properties. In addition to a brief discussion of exact results for the circular Wilson loop and the cusp…
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of…
In the present paper we extend the "torus gauge fixing approach" by Blau and Thompson (Nucl. Phys. B408(1):345--390, 1993) for Chern-Simons models with base manifolds M of the form M= \Sigma x S^1 in a suitable way. We arrive at a heuristic…
We perform a detailed study of the Yangian symmetry of smooth supersymmetric Maldacena-Wilson loops in planar N=4 super Yang-Mills theory. This hidden symmetry extends the global superconformal symmetry present for these observables. A…
To every compact oriented surface that is composed entirely out of 2-dimensional 0- and 1-handles, we construct a dg category using structures arising in Khovanov homology. These dg categories form part of the 2-dimensional layer (a.k.a.…
We study Coulomb branch (``u-plane'') integrals for $\mathcal{N}=2$ supersymmetric $SU(2),SO(3)$ Yang-Mills theory on 4-manifolds $X$ of $b_1(X)>0, b_2^+(X)=1$. Using wall-crossing arguments we derive expressions for the Donaldson…
A classical Wilson line is a cooresponedce between closed paths and elemets of a gauge group. However the noncommutative geometry does not have closed paths. But noncommutative geometry have good generalizations of both: the covering…
We define and study the properties of observables associated to any link in $\Sigma\times {\bf R}$ (where $\Sigma$ is a compact surface) using the combinatorial quantization of hamiltonian Chern-Simons theory. These observables are traces…
We study the issue of gauge-invariant observables in d=4, N=4 noncommutative gauge theory and UV-IR relation therein. We show that open Wilson lines form a complete set of gauge invariant operators, which are local in momentum space and,…
The path integral generalization of the Casson invariant as developed by Rozansky and Witten is investigated. The path integral for various three manifolds is explicitly evaluated. A new class of topological observables is introduced that…
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…
The $N=2$ topological Yang-Mills and holomorphic Yang-Mills theories on simply connected compact K\"{a}hler surfaces with $p_g\geq 1$ are reexamined. The $N=2$ symmetry is clarified in terms of a Dolbeault model of the equivariant…
We study a recently discovered family of 1/8-BPS supersymmetric Wilson loops in N=4 super Yang-Mills theory and their string theory duals. The operators are defined for arbitrary contours on a two-sphere in space-time, and they were…
Some exact expressions for non-selfintersecting Wilson loops in Yang Mills theory on the infinite plane are reviewed.
We study the rich dynamics resulting from introducing static charged particles (Wilson lines) in 2+1 and 3+1 dimensional gauge theories. Depending on the charges of the external particles, there may be multiple defect fixed points with…
In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…
We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the…
We derive an action describing edge dynamics on interfaces for gauge theories (Maxwell and Yang-Mills) using the path integral. The canonical structure of the edge theory is deduced and the thermal partition function calculated. We test the…
Previous path integral treatments of Yang-Mills on a Riemann surface automatically sum over principal fiber bundles of all possible topological types in computing quantum expectations. This paper extends the path integral formulation to…