Related papers: Direct and Indirect Loop Equations in Lattice Yang…
We introduce a comprehensive framework for analyzing finite $N$ lattice Yang-Mills theory and finite $N$ matrix models. Utilizing this framework, we examine the bootstrap approach to SU(2) Lattice Yang-Mills Theory in 2,3 and 4 dimensions.…
We apply the positivity bootstrap approach to SU(3) lattice Yang-Mills (YM) theory, extending previous studies of large N and SU(2) theories by incorporating multiple-trace Wilson loop operators. By utilizing Hermitian and reflection…
We study the $SU(\infty)$ lattice Yang-Mills theory at the dimensions $D=2,3,4$ via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with a cut-off $L_{\mathrm{max}}$ on the maximal length of loops, and…
The uniquess of the effective actions describing 4D SU(2) and SU(3) continuum, infinite-volume Yang-Mills thermodynamics in their deconfining and preconfining phases is made explicit. Subsequently, the spatial string tension is computed in…
We identify a universal finite-$N$ structure underlying Wilson loop expectations in lattice Yang-Mills, in any dimension $d\geq 2$, for gauge group $\mathrm{U}(N)$, and for arbitrary smooth central plaquette actions. The starting point is a…
The Schwinger-Dyson equations of the Makeenko-Migdal type, when supplemented with some simple equations as consequence of supersymmetry, form a closed set of equations for Wilson loops and related quantities in the two dimensional…
We use Schwinger Bosons as prepotentials for lattice gauge theory to define local linking oper- ators and calculate their action on linking states for 2 + 1 dimensional SU(2) lattice gauge theory. We develop a diagrammatic technique and…
We derive Wong's equations for the finite-dimensional dynamical system representing the motion of a scalar particle on a compact Riemannian manifold with a given free isometric smooth action of a compact semisimple Lie group. The obtained…
The paper establishes a direct linearization scheme for the SU(2) anti-self-dual Yang-Mills (ASDYM) equation.The scheme starts from a set of linear integral equations with general measures and plane wave factors. After introducing…
A derived algebraic geometric study of classical $\mathrm{GL}_n$-Yang-Mills theory on the $2$-dimensional square lattice $\mathbb{Z}^2$ is presented. The derived critical locus of the Wilson action is described and its local data supported…
We analyze quantum Yang-Mills theory on $\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is…
We explore the phase diagram of the SU(2) Yang-Mills theory in 5 dimensions by numerical simulations. The lattice system shows a dimensionally-reduced phase where the extra dimension is small compared to the four dimensional correlation…
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 derive an infinite sequence of Schwinger-Dyson equations for $N=1$ supersymmetric Yang-Mills theory. The fundamental and the only variable employed is the Wilson-loop geometrically represented in $N=1$ superspace: it organizes an…
We derive a form of master loop equations for the lattice Yang-Mills-Higgs theory with structure group $SO(N)$, $U(N)$ or $SU(N)$. Compared to the pure Yang-Mills setting, several new operations arise. In fact, to obtain a closed recursion…
We study our Schwinger-Dyson equation as well as the large $N_{c}$ loop equation for supersymmetric Yang-Mills theory in four dimensions by the N=1 superspace Wilson-loop variable. We are successful in deriving a new manifestly…
Pure gauge theories can be formulated in terms of Wilson Loops correlators by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In particular, using the lattice as a regulator,…
We formulate a nonsingular loop-space calculus for Yang-Mills (YM) gradient flow directly in terms of Wilson loops. Variations act within the manifold of smooth loops via finite, reparametrization-invariant "dot derivatives," eliminating…
The N=(2,2) extended super Yang-Mills theory in 2 dimensions is formulated on the lattice as a dimensional reduction of a 4 dimensional lattice gauge theory. We use the plaquette action for a bosonic sector and the Wilson- or the…
In this paper we provide a geometric derivation of the master loop equation for the lattice Yang-Mills model with structure group $G \in \{SO(N),SU(N), U(N)\}$. This approach is based on integration by parts on $G$. In the appendix we…