Daily Run: Connes' Standard Model

Day 1

Noncommutative gauge algebra

1. Used Python to sum the dimensions of $U(1)$, $SU(2)$, and $SU(3)$, obtaining a 12‑dimensional gauge algebra.
2. Checked each factor individually—$1+3+8$—matching the spectral triple's finite algebra.
3. Prepared these dimensions for insertion into the spectral action expansion.

Supersymmetric extension: squarks and sleptons

1. Enumerated squark multiplets per generation (left doublet and right singlets) yielding 12 complex scalars each.
2. Listed slepton partners including right‑handed neutrinos for 4 fields per generation.
3. Computed totals with Python: 36 squarks, 12 sleptons, 48 sfermion fields to add to the action.

Yukawa matrix structure

1. Generated a random $3\times3$ Yukawa matrix and evaluated its determinant numerically.
2. The determinant $\det Y \approx 0.44$ sets the overall scale for flavor mixing terms.
3. Noted that non-zero determinant ensures three distinct mass eigenvalues.