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The Schrodinger wave functional for the d=3+1 SU(N) vacuum is a partitionfunction constructed in d=4; the exponent 2S in the square of the wavefunctional plays the role of a d=3 Euclidean action. We start from agauge-invariant conjecture for the infrared-dominant part of S, based ondynamical generation of a gluon mass M in d=4. We argue that the exact leadingterm, of O(M), in an expansion of S in inverse powers of M is a d=3gauge-invariant mass term (gauged non-linear sigma model); the next leadingterm, of O(1/M), is a conventional Yang-Mills action. The d=3 action that isthe sum of these two terms has center vortices as classical solutions. The d=3gluon mass, which we constrain to be the same as M, and d=3 coupling arerelated through the conjecture to the d=4 coupling strength, but at the sametime the dimensionless ratio in d=3 of mass to coupling squared can beestimated from d=3 dynamics. This allows us to estimate the QCD coupling$\alpha_s(M^2)$ in terms of this strictly d=3 ratio; we find a value of about0.4, in good agreement with an earlier theoretical value but a little lowcompared to QCD phenomenology. The wave functional for d=2+1 QCD has anexponent that is a d=2 infrared-effective action having both thegauge-invariant mass term and the field strength squared term, and so differsfrom 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-grouprepresentations. But with the mass term (again leading to center vortices),N-ality = 0 mod N representations are not confined.Comment: 15 pages, no figures, revtex

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