M Theory Lesson 262

Using only integer values for the squares of entries in 27 $F^{†}VF$, it follows that the small (squares of) entries in the imaginary part must sum to 3. On solving for the variables $I$, $J$, $K$, $R$, $G$ and $B$ one has the freedom of signs in sorting out the CKM values.

Let us just look at the up-down entry, $I+iR$. The solution is given by

$3I=26+2\sqrt{697}$
$3R=\sqrt{53}-2\sqrt{2}$

and so the up-down entry $V_{ud}$ must equal $0.9744=\sqrt{I^2+R^2}$. Fortunately, according to wikipedia, this value is $0.9742\pm 0.0002$. It should not be difficult for the reader to find expressions for the other CKM entries, based on the Fourier transform.

Aside: Tommaso Dorigo continues with his excellent series of posts on fairy fields.