A conjecture on the infrared structure of the vacuum Schrodinger wave functional of QCD

TL;DR

This paper proposes a gauge-invariant infrared structure for the QCD vacuum wave functional, linking a dynamical gluon mass to a three-dimensional effective action with center vortices, and estimates the strong coupling constant.

Contribution

It introduces a novel gauge-invariant conjecture for the infrared dominant part of the QCD vacuum wave functional based on a dynamical gluon mass and connects 3D effective actions to 4D QCD properties.

Findings

Estimated the QCD coupling constant as approximately 0.4.

Identified the leading infrared term as a gauge-invariant mass term.

Showed that center vortices emerge as classical solutions in the effective 3D action.

Abstract

The Schrodinger wave functional for the d=3+1 SU(N) vacuum is a partition function constructed in d=4; the exponent 2S in the square of the wave functional plays the role of a d=3 Euclidean action. We start from a gauge-invariant conjecture for the infrared-dominant part of S, based on dynamical generation of a gluon mass M in d=4. 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 non-linear sigma model); the next leading term, of O(1/M), is a conventional Yang-Mills action. The d=3 action that is the sum of these two terms has center vortices as classical solutions. The d=3 gluon mass, which we constrain to be the same as M, and d=3 coupling are related through the conjecture to the d=4 coupling strength, but at the same time the dimensionless ratio in d=3 of mass to coupling squared can be estimated 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 about 0.4, in good agreement with an earlier theoretical value but a little low compared to QCD phenomenology. 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), N-ality = 0 mod N representations are not confined.