Orbifold explorer · SU(4) gauge–Higgs on T²/ℤ₂

One bit decides what your potential can contain

Pick a representation. The Wilson-line potential, the harmonics it is allowed to carry, and whether you may halve your search region all follow from the parity of one number. Everything runs in your browser.

Representation

Landscape — click any cell

even-m comb odd-m comb degenerate ◯ hosts a quark generation

Across the catalogue

Every representation with a+b+c ≤ 7 and dimension ≤ 3000.

One-loop Wilson-line potential over the period-2 torus

three views of the same field — drag the 3D ones to rotate

Twist imbalance δ(m)

Fourier support — the seats that stay empty

What is proved, what is measured

Part IV — the compression to three integers

Beyond SU(4) — measure instead of assume

Everything above is a theorem, and only for $SU(4)$ on T²/ℤ₂. For any other spectrum there is no theorem, so the pairings have to be measured. That is what this panel does, and it is the part of this page that a formula cannot replace.

One row per tower: m, q, multiplicity. Both combs are measured directly, so this stays valid for any group and any orbifold.

One row per diagonal slot of the group element your orbifold hands you: twist sign (±1), Wilson-line charge. A centre-parity rule exists only if a unit shift is Weyl-equivalent to a central element.