Related papers: Wilson loop expectations in lattice gauge theories…
Wilson loop expectation in 4D $\mathbb{Z}_2$ lattice gauge theory is computed to leading order in the weak coupling regime. This is the first example of a rigorous theoretical calculation of Wilson loop expectation in the weak coupling…
We consider lattice gauge theories on $\mathbb{Z}^4$ with Wilson action and structure group $\mathbb{Z}_n$. We compute the expectation of Wilson loop observables to leading order in the weak coupling regime, extending and refining a recent…
Lattice Gauge theories have been studied in the physics literature as discrete approximations to quantum Yang-Mills theory for a long time. Primary statistics of interest in these models are expectations of the so called "Wilson loop…
We consider the lattice Higgs model on $\mathbb{Z}^4$, with structure group given by $ \mathbb{Z}_n $ for $ n \geq 2 $. We compute the expected value of the Wilson loop observable to leading order when the gauge coupling constant and…
The main result of this paper is a rigorous computation of Wilson loop expectations in strongly coupled $SO(N)$ lattice gauge theory in the large $N$ limit, in any dimension. The formula appears as an absolutely convergent sum over…
This article gives a rigorous formulation and proof of the $1/N$ expansion for Wilson loop expectations in strongly coupled $SU(N)$ lattice gauge theory in any dimension. The coefficients of the expansion are represented as absolutely…
We consider the 4D fixed length lattice Higgs model with Wilson action for the gauge field and structure group $\mathbb{Z}_n$. We study Wilson line observables in the strong coupling regime and compute their asymptotic behavior with error…
We consider computations of Wilson loop expectations to leading order at large $\beta$ in the case where a non-abelian gauge field interacts with a Higgs boson. By identifying the main order contributions from minimal vortices, we can…
Lattice gauge theories are lattice approximations of the Yang-Mills theory in physics. The abelian lattice Higgs model is one of the simplest examples of a lattice gauge theory interacting with an external field. In a previous…
We present an application of the standard Langevin dynamics to the problem of weak coupling perturbative expansions for Lattice QCD. This method can be applied to the computation of the most general observables. In this preliminary work we…
In this paper, we obtain bounds on the Wilson loop expectations in 4D $U(1)$ lattice gauge theory which quantify the effect of topological defects. In the case of a Villain interaction, by extending the non-perturbative technique introduced…
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 calculate Wilson loops of various sizes up to 20 loops in SU(3) pure lattice gauge theory at different lattice sizes for Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate…
Wilson loops provide the central gauge-invariant probe of confinement in lattice gauge theory. This survey reviews the statistical-mechanical formulation of lattice gauge ensembles, the strong-coupling and duality mechanisms behind area…
In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary…
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 develop a powerful framework to calculate expectation values of polynomials and moments on compact Lie groups based on elementary representation-theoretic arguments and an integration by parts formula. In the setting of lattice gauge…
The stochastic vacuum model description of a heavy meson is discussed in the context of a gauge invariant approach where Wilson loop expectation values appear naturally in the O($v^2$) spin-orbit Hamiltonian. These expectation values have…
We consider the Wilson loop expectation in SU(2) lattice gauge theory in the presence of constraints. The constraints eliminate from the functional measure gauge field configurations whose physical interpretation is that of thick center…
In this article, we further explore the construction and computation of expectation values for Wilson loops in higher-rank 5d $\mathcal{N} = 1$ gauge theories on $\mathbb{C}_2 \times S_1$, by explicitly computing the Wilson loops via…