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Order Parameters for Confinement

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An Introduction to the Confinement Problem

Part of the book series: Lecture Notes in Physics ((LNP,volume 972))

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Abstract

The Wilson loop, Polyakov loop, and ‘t Hooft loop as order parameters for confinement. Wilson loops and the propagation of heavy quark-antiquark pairs, Polyakov loops and finite temperature gauge theories, ‘t Hooft loops as center vortex creation operators, and the center vortex free energy. The topological linking of center vortices with Wilson loops. The relation between order parameters for confinement, and center symmetry.

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Notes

  1. 1.

    The notation, while standard, is potentially confusing, because β is also used for lattice coupling, and T for time; so I emphasize again that in this section T stands for temperature, not time. In fact, as we will see, it is β which represents a time extension.

  2. 2.

    We note again that an order parameter for the spontaneous breaking of a global symmetry, such as 〈P(x)〉, is only non-zero, strictly speaking, in the infinite volume limit. In practice what is done is to compute, on each lattice, the magnitude of the sum of Polyakov loops of the lattice, divided by the number of loops (cf. (6.65) below). The expectation value of this quantity, which is guaranteed to be positive, is then extrapolated to the infinite volume limit, and if the limit is vanishing, the symmetry is unbroken.

References

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Greensite, J. (2020). Order Parameters for Confinement. In: An Introduction to the Confinement Problem. Lecture Notes in Physics, vol 972. Springer, Cham. https://doi.org/10.1007/978-3-030-51563-8_4

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