# Questions tagged [wilson-loop]

In gauge theory, a Wilson loop is a gauge-invariant observable obtained from the holonomy of the gauge connection around a given (closed) loop $C$. It is the trace of a path-ordered exponential of the gauge field $A_\mu$ transported along $C$, $W_C := \mathrm{Tr}(\mathcal{P}\exp i \oint_C A_\mu dx^\mu)$, where $\mathcal{P}$ is the path-ordering operator.

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### How can I find the third spectrum of lines in $SU(2)$ gauge theory?

In the article https://arxiv.org/abs/1305.0318, they take a gauge theory based on the algebra $su(2)$ as a first example of how to determine the allowed line operators. Once different lines can be ...
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### Vacuum expectation value of the Wilson loop in pure QED

In Chapter 57 of Srednicki's QFT book he derives the generating function of pure QED and finds \begin{align*} Z(J) = \exp\left[\frac{i}{2}\int\mathrm{d}^4x\,\mathrm{d}^4y\ J_\mu(x) \Delta^{\mu\nu}(x-y)...
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### Wilson loops as representations of the Lorentz group

Wilson loops in lattice $4d$ Yang-Mills theory are used to build various glueball states of different spins when they are applied to the vacuum. The spin dependence of such states is related with the ...
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### Area and perimeter

Apparently (?), a line operator over a very large loop with length $L$ can obey either perimeter law or area law, $-\log\langle U\rangle\sim L^a$ with $a=1,2$, respectively. We call these options &...
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### Expand an infinitesimal Wilson loop

I have a question about expanding an infinitesimal Wilson loop operator to get the field tensor $F_{\mu \nu}$ in chapter 3 of Fradkin's notes Classical Symmetries and Conservation Laws. For a ...
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### Wilson loop shapes and glueball operators

In the AdS/QCD correspondence, glueballs operators are given, for example, by $\text{Tr}[F_{\mu \nu}F^{\mu \nu}]$ for $0^{++}$ or $\text{Tr}[F_{\mu \nu}\widetilde{F}^{\mu \nu}]$ for $0^{-+}$. However, ...
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### Connection between Wilson loops and fusion rules in $Z_2$ topological order

I'm looking for references (reviews, original articles, lecture notes, etc.) that discuss the connection between the expectation value of Wilson loops (the "disorder parameter" of the system) and ...
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### Wilson loop as path integral of parallel transport action

I am trying to get that the path integral of the parallel transport action is the Wilson loop. Here is the setting: Let $w$ be a complex vector dimension $N$, and $A_{\mu}$ a fixed Yang-Mills ...
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### Derivative of a Wilson Line

It's my first post on this website so please excuse any breaches of protocol that I'm unaware of. I've come across a formula for taking derivatives of Wilson Lines with respect to points on the path,...
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In chapter 82 https://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf Srednicki comes to the following form for the Wilson loop for free electromagnetic theory: \langle 0|W_C|0\rangle=\exp\left[-\frac{...
I'm trying to prove that the Wilson loop operator is well-defined in non-interacting quantum electrodynamics without matter, that is, $\hat{W}(\gamma)$ is a bounded operator on the Hilbert space. ...