Yang-Mills Constructive QFT Literature Map¶

Balaban Program (1984-1998)¶

1984-85: RG infrastructure, propagators, renormalization transforms, 3D UV stability
1987-88: 4D small-field cluster expansion (Parts I-II), large-field intro for superrenormalizable models
1989: Large Field Renormalization I-II — R-operation completes 4D UV stability
1990: Constructive Gauge Theory II (survey)
1995-98: O(N)/N-vector applications, large-field operation in different settings

MRS (Magnen-Rivasseau-Sénéor) 1993¶

Construction of YM_4 with infrared cutoff, Commun. Math. Phys. 155
Regularized axial gauge, nonperturbative stabilization around large backgrounds
IR cutoff retained, different stabilization mechanism from Balaban

Chatterjee Program (2016-present)¶

2016: Yang-Mills for probabilists (framework)
2020: Wilson-loop calculation in 4D Z_2 lattice gauge theory (weak coupling)
2021: Confinement from unbroken center symmetry
Later: State-space/heat-flow work, distributional gauge orbits
KEY WALL: 4D is critical for YM heat flow, probabilistic smoothing fails

What Nobody Has Done¶

No one has constructed nonabelian Euclidean YM in d≥3 as a probability measure on connections/gauge orbits AND constructed physically relevant observables (Cao-Chatterjee assessment).