Glueba

Glueba is a knot of looped gluon flux: made of massless threads, and yet, it seems, heavy.

The Physics

Yang and Mills wrote down gauge theories with non-commuting symmetry groups in 1954. Their quanta are massless at the classical level and interact with each other. In quantum theory, pure SU(3) Yang–Mills (QCD without quarks) is believed to confine and to have a mass gap: the lightest excitation has strictly positive mass.

Nobody has proved it. Lattice computer simulations support the gap: Morningstar and Peardon (1999) put the lightest pure-gauge glueball near 1.7 GeV.

Prove: quantum Yang–Mills exists on R⁴ and has a mass gap Δ > 0

• R⁴: four-dimensional spacetime
• Δ: mass of the lightest excitation above the vacuum
• Gauge group G: any compact simple group (Clay statement)

Yang & Mills, Phys. Rev. 96, 191 (1954). The Clay Mathematics Institute listed the problem among its Millennium Prize Problems in 2000, in a statement by Jaffe and Witten.

Honest caveat: This problem is UNSOLVED. The 1.7 GeV figure is a lattice estimate for a theory with no quarks, not a proof and not the gap itself. Glueballs in the real world, with quarks present, have not been conclusively identified.

On the shirt

Front: Glueba, the pixel-art character, with “MIND THE GAP”. Back: the Clay problem statement, the lattice glueball hint, the UNSOLVED label and Yang & Mills 1954. Printed on a unisex tee.