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What Is 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

Confinement and symmetry. Linear Regge trajectories, the linear static quark potential, and the “spinning stick” model. String breaking, existence of “color confinement” in the Higgs phase, and the difficulty of associating confinement with an unbroken or spontaneously broken remnant gauge symmetry. Confinement as magnetic disorder; center symmetry as the global symmetry corresponding to the confined phase.

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Notes

  1. 1.

    What this means is that the order parameter for the transition can be non-zero in the infinite 3-volume limit at any fixed time, but have different values at different times, averaging to zero if we average over all times. Thus the symmetry can be spontaneously broken on any single timeslice, or finite set of timeslices, without violating the Elitzur theorem.

  2. 2.

    The Clay Mathematics Institute offers a large cash prize (http://www.claymath.org/millennium/Yang-Mills_Theory) for proving that Yang-Mills theory has a mass gap, which would be true in any gauge theory which is in either a magnetically disordered phase, as in pure Yang-Mills theory, or a massive phase, as in Higgs theories and in real QCD.

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Greensite, J. (2020). What Is 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_3

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