Establish color confinement within the spontaneous BRST‑breaking framework

Determine whether color confinement is realized within the effective model featuring spontaneous BRST and anti‑BRST symmetry breaking, for example by verifying if the Kugo–Ojima confinement criterion can be satisfied in the infrared, and characterize the mechanism that eliminates colored states from the physical spectrum.

Background

The paper articulates an effective low-energy framework where spontaneous BRST and anti‑BRST breaking generates effective masses and introduces massless Nambu–Goldstone modes, potentially relevant to the quartet mechanism that removes unphysical states.

They explicitly identify the confinement problem as an outstanding issue and mention the Kugo–Ojima criterion as a rigorous benchmark, suggesting that the introduced Nambu–Goldstone modes might be instrumental in realizing confinement within this framework.

References

The ultimate question of color confinement is left for future work, though our framework provides a promising path for its resolution.

— Spontaneous BRST symmetry breaking in infrared QCD  (2603.29401 - Fazio et al., 31 Mar 2026) in Conclusions, paragraph 4

A remaining important problem is to show explicitly that in the channels of the BRST and anti-BRST transformations of the massive ghost, bound states are really formed by some ingenious non-local and/or non-perturbative effects.

— Massive Ghost Confinement, Dipole Equation and Multipole States in Quadratic Gravity  (2608.26085 - Oda, 26 Aug 2026) in Section 6, Conclusions