Amplituhedron and E8

  • #1
tionis
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Main Question or Discussion Point

Hi. I've been watching Nima's lectures on the Amplithedron, and have followed Lisi's E8 theory as well. While not able to understand them in a rigorous way, I'm fascinated by these two geometric objects and I'm wondering if the two could be combined, or if you could derive one from the other. I would also like to know what overlaps (if any), are between these two objects and strings. Which one would be/is more fundamental between the three.

Thanks!
 

Answers and Replies

  • #2
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The original amplituhedron describes aspects of a field theory with a gauge symmetry and four supersymmetries. Such field theories do appear in string theory in various ways so there is definitely a relationship to string theory.

There are also various ways that a field with E8 symmetry can appear in string theory, and some of them are considered candidates to describe the real world.

Field theory and string theory are already known to admit many unexpected alternative descriptions - symmetries, dualities, etc. So far the amplituhedron offers only an incomplete description of some field theories with a high degree of supersymmetry. It may be a glimpse of something more general, but if so that is not yet worked out.

"E8 theory" is a hope that not just the standard model, but also gravity, or even space-time itself, can be obtained from a single copy of E8. This hope has not been fulfilled so far, and the philosophy of "E8 theory" is somewhat at odds with the philosophy of string theory where gravity and space-time are concerned.
 
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  • #3
tionis
Gold Member
458
67
The original amplituhedron describes aspects of a field theory with a gauge symmetry and four supersymmetries. Such field theories do appear in string theory in various ways so there is definitely a relationship to string theory.

There are also various ways that a field with E8 symmetry can appear in string theory, and some of them are considered candidates to describe the real world.

Field theory and string theory are already known to admit many unexpected alternative descriptions - symmetries, dualities, etc. So far the amplituhedron offers only an incomplete description of some field theories with a high degree of supersymmetry. It may be a glimpse of something more general, but if so that is not yet worked out.

"E8 theory" is a hope that not just the standard model, but also gravity, or even space-time itself, can be obtained from a single copy of E8. This hope has not been fulfilled so far, and the philosophy of "E8 theory" is somewhat at odds with the philosophy of string theory where gravity and space-time are concerned.
Wow! Thanks, Mitchell Porter.
 

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