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.
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.
posted by Kea | 1:55 PM
2 Comments:
The story is continually exciting and adds to the M-theory lessons. Many features appear to correspond to the natural world.
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.
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