A mechanism for quark confinement
Published 2020-06-29Version 1
The confinement of quarks is one of the enduring mysteries of modern physics. This article shows that if a pure lattice gauge theory at some given coupling strength has exponential decay of correlations for local operators under arbitrary boundary conditions, and the gauge group is a compact connected matrix Lie group with a nontrivial center, then the theory is confining. The exponential decay assumption is stronger than usual mass gap, which means exponential decay under a specific boundary condition dictated by the Feynman path integral associated with the theory. The strengthening ensures that center symmetry is not spontaneously broken. This gives the first mathematical support for the longstanding belief in physics that mass gap plus unbroken center symmetry imply confinement. It also gives the first evidence that correlation decay for local operators can prevent the breaking of center symmetry and cause confinement. The main step in the argument uses correlation decay for local operators to deduce correlation decay for certain nonlocal operators similar to Polyakov loops. The proof is almost entirely based in probability theory, making extensive use of the idea of coupling probability measures.