# Arcadian Functor

occasional meanderings in physics' brave new world

Name:
Location: New Zealand

Marni D. Sheppeard

## Friday, November 16, 2007

### M Theory Lesson 125

The $D_4$ triality in Garrett's paper (slide 16) leaves invariant the $W^{3}$. Deleting this component of the $4 \times 4$ rotation matrix reduces it to the matrix

010
001
100

which is the $(231)$ Fourier basis $3 \times 3$ circulant familiar to M theorists. Observe that this matrix permutes the $\frac{1}{2} \omega_{R}^{3}$, $\frac{1}{2} \omega_{L}^{3}$ and $B_{1}^{3}$ gravity fields.

#### 2 Comments:

L. Riofrio said...

The story is continually exciting and adds to the M-theory lessons. Many features appear to correspond to the natural world.

November 17, 2007 9:08 AM
Kea said...

Thanks, Louise. Yes, surely particle masses are one of the most basic things we can measure. It is time we understood where they came from.

November 18, 2007 8:08 AM