Wilson loop

<p>In <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, Wilson loops are <a href="/facts/Introduction_to_gauge_theory/CJf77mlR">gauge invariant</a> operators arising from the <a href="/facts/Parallel_transport/QX0Wfcte">parallel transport</a> of gauge variables around closed <a href="/facts/Loop_(topology)/mgtE53Ty">loops</a>. They encode all gauge information of the theory, allowing for the construction of <a href="/facts/Loop_representation_in_gauge_theories_and_quantum_gravity/YvXzeh6W">loop representations</a> which fully describe <a href="/facts/Gauge_theory/fSW3gggv">gauge theories</a> in terms of these loops. In pure gauge theory they play the role of <a href="/facts/Order_operator/3lvncssb">order operators</a> for <a href="/facts/Color_confinement/W3XjqMAS">confinement</a>, where they satisfy what is known as the area law. Originally formulated by <a href="/facts/Kenneth_G._Wilson/BSSajpeo">Kenneth G. Wilson</a> in 1974, they were used to construct links and plaquettes which are the fundamental parameters in <a href="/facts/Lattice_gauge_theory/90xxuLpx">lattice gauge theory</a>. Wilson loops fall into the broader class of loop <a href="/facts/Operator_(physics)/rCJw8UFz">operators</a>, with some other notable examples being <a href="/facts/%27t_Hooft_loop/xxAEoDQR">'t Hooft loops</a>, which are magnetic duals to Wilson loops, and <a href="/facts/Polyakov_loop/Wz089unD">Polyakov loops</a>, which are the thermal version of Wilson loops.
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Wilson loop open-in-new

Wilson loop