Abstract
There are certain observables whose behavior indicates that a gauge system is, or is not, in a phase of magnetic disorder. These are the Wilson loop, the Polyakov loop, the ‘t Hooft loop, and the vortex free energy. The Wilson loop has been discussed already, to some extent. The Polyakov loop is a Wilson loop which winds around a finite, periodic lattice in the time direction; it is a crucial probe of center symmetry and the high temperature deconfinement phase transition, in which center symmetry is spontaneously broken. The ‘t Hooft loop is an operator which creates an object known as a center vortex. The center vortex scenario for confinement will be discussed in some detail in Chaps. 6 and 7.
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- 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.
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. 6.62) in (Chap. 6) . 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.
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Greensite, J. (2010). Order Parameters for Confinement. In: An Introduction to the Confinement Problem. Lecture Notes in Physics, vol 821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14382-3_4
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DOI: https://doi.org/10.1007/978-3-642-14382-3_4
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