Conjecture on the infrared structure of the vacuum Schrödinger wave functional of QCD

The Schrödinger wave functional ψ=exp⁡(-S{A_i^a(x⃗)}) for the d=3+1 QCD vacuum is a partition function constructed in d=4; the exponent 2S [in |ψ|²=exp⁡(-2S)] plays the role of a d=3 Euclidean action. We start from a simple conjecture for S based on dynamical generation of a gluon mass M in d=4, then use earlier techniques of the author to extend (in principle) the conjectured form to full non-Abelian gauge invariance. We argue that the exact leading term, of O(M), in an expansion of S in inverse powers of M is a d=3 gauge-invariant mass term (gauged nonlinear sigma model); the next-leading term, of O(1/M), is a conventional Yang-Mills action. The d=3 action that is (twice) the sum of these two terms has center vortices as classical solutions. The d=3 gluon mass m₃, which we constrain to be the same as M, and d=3 coupling g₃² are related through the conjecture to the d=4 coupling strength, but at the same time the dimensionless ratio m₃/g₃² can be estimated from d=3 dynamics. This allows us to estimate the d=4 coupling α_s(M²) in terms of the strictly d=3 ratio m₃/g₃²; we find a value of about 0.4, in good agreement with an earlier theoretical value but somewhat low compared to the QCD phenomenological value of 0.7±0.3. The wave functional for d=2+1 QCD has an exponent that is a d=2 infrared-effective action having both the gauge-invariant mass term and the field-strength squared term, and so differs from the conventional QCD action in two dimensions, which has no mass term. This conventional d=2 QCD would lead in d=3 to confinement of all color-group representations. But with the mass term (again leading to center vortices), only N-ality≢0 mod N representations can be confined [for gauge group SU(N)], as expected.