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A Probabilistic Mechanism for Quark Confinement

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Abstract

The confinement of quarks is one of the enduring mysteries of modern physics. There is a longstanding physics heuristic that confinement is a consequence of ‘unbroken center symmetry’. This article gives mathematical confirmation of this heuristic, by rigorously defining of center symmetry in lattice gauge theories and proving that a theory is confining when center symmetry is unbroken. Furthermore, a sufficient condition for unbroken center symmetry is given: It is shown that if the center of the gauge group is nontrivial, and correlations decay exponentially under arbitrary boundary conditions, then center symmetry does not break.

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Acknowledgements

I thank Christian Borgs, Persi Diaconis, Jürg Fröhlich, Len Gross, Erhard Seiler, Senya Shlosman, Tom Spencer, Raghu Varadhan, and Akshay Venkatesh for helpful discussions. I am especially grateful to Edward Witten and Steve Shenker for many lengthy and illuminating conversations, and to Sky Cao for carefully reading the proof and pointing out some important references. Lastly, I thank the referees for a number of useful suggestions.

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  1. Departments of Mathematics and Statistics, Stanford University, Stanford, USA

    Sourav Chatterjee

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  1. Sourav Chatterjee
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Correspondence to Sourav Chatterjee.

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Communicated by M. Salmhofer

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Research was partially supported by NSF Grant DMS-1855484

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Chatterjee, S. A Probabilistic Mechanism for Quark Confinement. Commun. Math. Phys. 385, 1007–1039 (2021). https://doi.org/10.1007/s00220-021-04086-y

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