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Confinement from Center Vortices I

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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 center vortex confinement mechanism. Methods for locating center vortices in lattice configurations. Numerical evidence that center vortices are responsible for the asymptotic string tension.

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Notes

  1. 1.

    V μ(x) would also be responsible for “thickening” the flux of the thin vortices, so there must be some short range correlation between V μ(x) and vortex position.

  2. 2.

    The Creutz ratios χ[R, T] should not be confused with the group characters χ r[g] discussed previously.

  3. 3.

    Zakharov [20] has argued that surfaces with singular action density fit in well with the need for certain power corrections in QCD sum rules.

  4. 4.

    Another picture, in the Hamiltonian formulation, involves the notion of the Dirac sea. Under the influence of an external gauge field, the energy levels of the Dirac operator shift up or down, depending on the chirality of the state. This level-shifting can appear as the creation of quark-antiquark pairs by a gauge field, with quantum numbers violating conservation of the axial U(1) symmetry [26].

  5. 5.

    For a theory with N f massless flavors of quarks, the chiral symmetry is SU(N f)R × SU(N f)L, which is spontaneously broken to an SU(N f) flavor symmetry, and the massless Goldstone particles belong to a multiplet transforming in the adjoint representation of the remaining flavor symmetry.

  6. 6.

    It should be noted, however, that \(\langle \overline {\psi } \psi \rangle \) diverges like \(\log (m)\) in theories with no dynamical fermions, as m → 0.

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Greensite, J. (2020). Confinement from Center Vortices I. 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_6

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