• DOI:10.1103/PhysRevD.76.025012
• Corpus ID: 31502648

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

@article{Cornwall2007ConjectureOT,
  title={Conjecture on the infrared structure of the vacuum Schr{\"o}dinger wave functional of QCD},
  author={John M. Cornwall},
  journal={Physical Review D},
  year={2007},
  volume={76},
  pages={025012}
}

• J. Cornwall
• Published 7 February 2007
• Physics
• Physical Review D

The Schrodinger wave functional ψ = exp(-S(Aai)(x)}) 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 0(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 m 3 , which we constrain to be the same as M, and d = 3 coupling g2/3 are related through the conjecture to the d = 4 coupling strength, but at the same time the dimensionless ratio m 3 /g2/3 can be estimated from d = 3 dynamics. This allows us to estimate the d = 4 coupling α s (M 2 ) in terms of the strictly d = 3 ratio m 3 /g23; 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.