Emergent matter as form of ramification?

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Discussion Overview

The discussion explores the concept of emergent matter as a form of ramification, particularly in relation to braid relations and their potential connection to the internal symmetries of the Standard Model. Participants reference theoretical frameworks such as the Langland's program and loop quantum gravity (LQG), examining speculative ideas and ongoing research in this area.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the origins of braid relations, suggesting they do not arise naturally but are constructed to emulate the Standard Model.
  • Another participant mentions Yidun Wan and Jonathan Hackett as researchers who have explored the connection between braid relations and the Standard Model's internal symmetries.
  • A participant speculates about the nature of loop operators in LQG, comparing Wilson loop operators and t'Hooft/Wilson line operators in the context of Langland's dual gauge group.
  • There is a reference to the potential robustness of the principles underlying the correspondence discussed, despite limitations in existing papers that focus on specific cases of supersymmetry.

Areas of Agreement / Disagreement

Participants express differing views on the nature and origin of braid relations, with some suggesting they are constructed rather than naturally occurring. The discussion remains unresolved regarding the applicability of these concepts to the Standard Model and the specifics of loop operators in LQG.

Contextual Notes

Participants note the speculative nature of the discussion and the lack of explicit attempts to connect braid relations to supersymmetry, indicating a need for further exploration and understanding of the underlying theories.

Jim Kata
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Ok, I doubt this belongs in this forum since it's purely speculative, but I was curious what work has been done in the direction of explaining emergent matter as a type of ramification? Namely, Sundance Bilson showed in a novel paper that he could create the first generation of the Standard Model through braid relations. Now a natural question is why would these braid relations arise? In the tamely ramified Langland's program braid relations arise as the Weyl group of an affine lie algebra. They describe center of a universal cover of a group or the fundamental group of the adjoint representation of a group. Has anyone tried to work out the details as to whether this mechanism could explain the internal symmetries of the standard model?
 
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Jim Kata said:
Has anyone tried to work out the details as to whether this mechanism could explain the internal symmetries of the standard model?

Look on arxiv for the papers of Yidun Wan.

Yidun Wan is one of a handful of people who have been researching this idea in the past couple of years.
Jonathan Hackett is another.
 
Jim Kata said:
Now a natural question is why would these braid relations arise?
They don't arise. They are just made to eventualy emulate the SM. They are beautiful, though, and work in a very subtle way. Not at all naive.

As Marcus said, check Yin DunWan:
http://arxiv.org/find/hep-th/1/au:+Wan_Y/0/1/0/all/0/1


Jim Kata said:
Has anyone tried to work out the details as to whether this mechanism could explain the internal symmetries of the standard model?

I never saw any explicit attempt in considering any supersymmetry, much less N4SYM. But I was thinking about that too... About the ramified case of the langlands, but I am almost there in trying to understand the gist of it.

Anyway, what kind of loop operator is that one of LQG?
 
MTd2 said:
Anyway, what kind of loop operator is that one of LQG?

On one side of the correspondence it's a Wilson loop operator, which is an element of the fundamental group. On the other side of the correspondence it's a t'Hooft / Wilson line operator over the Langland's dual gauge group, through a type of magnetic monopole phenomena. I'm really just speculating, but this would be consistent with the Witten Kapustin description. Granted, their paper only considered a topologically twisted version of N=4 supersymmetry, but I think the under riding principles of the correspondence are more robust than just applying to the GL twisted N = 4 case.
 

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