Quantum Chromodynamics 2026, 14 - Ground State of QCD

The QCD ground state is not well known as of yet. This book presents the "Spaghetti vacuum" model, which it claims, is easily visualized. It emerges from the behavior of a monopole-antimonopole pair in a superconductor. Meissner-Ochsenfeld prevents the flux lines of a magnetic field from entering a superconducting region, so a stringy region of normal conduction is created between the pair. The magnetic charges are confined (p.515). The description of the QCD ground state is dual to this superconductivity picture, in which the magnetic and electric fields are interchanged and the Cooper pairs within the vacuum are strings of color magnetic fields. For this, a color magnetic background field H is introduced, and its vacuum energy calculated, assuming a homogeneous magnetic field. The specifics of the calculation are set by the gauge theory for the field-strength tensor, but it's usually assumed SU(2) (p. 516). The energy can become imaginary at root, which corresponds to a decay width, marking the state unstable. This contradicts the assumption of a homogeneous color magnetic field. Ignoring this, the single-particle energies follow the typical energy density (p. 519). Minimizing the real part of the vacuum energy H²/2, yields a minimum at H ≠ 0. The prefactor for the vacuum energy's renormalization group property derives from the gauge group's β-function (Eq. 8.33). A stable state can be obtained by isolating the unstable modes and rewriting the Lagrange density to have them appear as Higgs fields, and inserting nonvanishing vacuum expectation values and determine the energetically optimal gauge field configuration. The lowest Landau state extends over large spatial domains, so the H fields average out, eliminating the instabilities. Higher Landau states are more localized and experience a more constant H field, which lowers the energy. The fields oscillate around the solution of their classical field equations, guaranteeing Lorentz invariance over large enough spatial domains. The picture of a dual superconductor is further supported by lattice calculations for some simple systems.