Mathematical proof of confinement in QCD

Prove confinement in four-dimensional pure SU(3) Yang–Mills gauge theory in the sense that only color-singlet states appear in the physical spectrum, thereby establishing the weak form of confinement referenced by the Clay Mathematics Institute’s prize problem.

Background

The paper reviews the complementary phenomena of freedom and confinement in QCD and notes the persistent intellectual tension between them. Although heuristic arguments and lattice evidence support confinement, a rigorous mathematical proof is still lacking. The Clay Mathematics Institute has highlighted this gap by offering a prize for a related formal result.

This problem seeks a precise, non-perturbative demonstration within the framework of pure SU(3) Yang–Mills theory that colored states are excluded from the spectrum, formalizing the confinement phenomenon that underpins hadron physics.