### M Theory Lesson 291

Many thanks to Mottle for pointing out the new S matrix paper by Arkani-Hamed et al.

Even more interesting, Mottle also points to this paper on Grassmanians. Having previously expressed some disgust at the idea of category theory in physics, he may not have noticed the intriguing references to operads.

Even more interesting, Mottle also points to this paper on Grassmanians. Having previously expressed some disgust at the idea of category theory in physics, he may not have noticed the intriguing references to operads.

## 5 Comments:

The morning e-mail brought another invite to a "Grassmanian Conference" in Poland Sept 14-18. Paris is closer.

A delightful paper indeed. I especially enjoyed this bit:

As stressed in [9], gravity amplitudes have a far richer structure than in Yang-Mills theory. They are governed by much larger “obvious” symmetries: instead of cyclic invariance, supergravity amplitudes have permutation symmetry, and instead of having the massless scattering amplitudes only defined at the origin of moduli space as for N = 4 SYM, the N = 8 SUGRA S Matrix is defined everywhere on moduli space and is non-trivially acted on by the E7(7) symmetry [9, 88, 89].Enjoy Rio, Louise! I liked the bit:

We are still missing a real understanding of the physics behind our conjecture. A clue is perhaps provided by the nature of the space in which it is formulated. Instead of spacetime, for n particle scattering the dual is naturally formulated in an n dimensional space ... we are finding that our dual picture isn't associated with a space in which particles live at all.I also found this part of interest:

Indeed we can focus on the G(k − 2, n − 4) space, “punctured” by removing the zero locus defined by the vanishing of the minor factors; the contours defining the amplitudes are then associated with non-trivial homology classes in this space.It seems they are working with the Grassmannian G(k - 2, n - 4) with the Segre variety removed. This type of geometry also appears in studies of abstract entanglement of n qubits.

Indeed, the growing connection between entanglement and twistor geometry is an exciting part of M Theory!

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