Topological Compressibility of the Yang-Mills Vacuum: A Semiclassical Prediction for Lattice QCD

Abstract

We treat the areal density of centre vortices as the order parameter of a homogeneous Ginzburg-Landau functional for the SU(3) vacuum. The quadratic coefficient is fixed, with no free parameters, by the one-loop thick-vortex effective action of Diakonov and Maul, which is negative and therefore destabilises the perturbative vacuum. The quartic coefficient — the repulsive core interaction, which we call the Vacuum Suppression Law (VSL) term — is fixed by the physical string tension. The resulting condensate reproduces the measured vortex areal density of 3.3 fm⁻² without further adjustment. The functional then predicts, with no remaining freedom, a collective amplitude mode of the vortex condensate at m₀ = 166 ± 13 MeV, equivalently ξ = 1.19 ± 0.09 fm. We show this mode cannot be a pole in any gauge-invariant scalar channel — the lattice excludes glueballs below ≈1.6 GeV — and argue that it should instead appear as the correlation length of the connected P-vortex density correlator measured in direct maximal centre gauge. We give an explicit falsification band and a measurement protocol. We also derive a second, independent consequence: the compressibility sum rule relates the same quantity to the volume dependence of the 't Hooft magnetic flux free energy under Z(3)-twisted boundary conditions. The prediction is sharp, cheap to test on existing configurations, and falsifiable in one measurement.