M-theory and Calabi-Yau compactifications

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Discussion Overview

The discussion revolves around the relationship between gauge groups, specifically SU(2) and U(2), and Calabi-Yau compactifications within the context of string theory and M-theory. Participants explore how these concepts interrelate, particularly in terms of principal bundles, gauge symmetries, and the implications for particle physics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants inquire about the connection between Calabi-Yau compactifications and gauge groups like SU(2), questioning whether Calabi-Yau compactifications can give rise to such groups.
  • One participant notes that d=6 Calabi-Yau spaces are relevant in d=10 string theory, while d=11 M-theory uses d=7 G2 manifolds, suggesting a hierarchy in dimensionality and their respective roles in gauge group formation.
  • Another participant describes two primary methods for obtaining gauge groups in string theory: using brane stacks and breaking larger intrinsic gauge groups, emphasizing that only the latter involves the Calabi-Yau structure.
  • Discussion includes the role of the Dirac operator on compact manifolds and its relation to particle physics, particularly in counting fermion families in heterotic models.
  • Some participants discuss the differences between gauge theory bundles and compact spaces in Kaluza-Klein and string/M theory, highlighting that gauge bundles are not extra dimensions but geometric objects associated with spacetime points.
  • There are inquiries about the relationship between gauge groups and the symmetries of compact manifolds, with references to specific examples like S^2 and its isometry group, as well as the potential for constructing manifolds with desired isometry groups.
  • Participants express curiosity about the concept of associated bundles and their connection to the Higgs field, seeking further details and references.

Areas of Agreement / Disagreement

Participants express a range of views on the connections between gauge groups and Calabi-Yau compactifications, with no consensus reached on the specifics of these relationships. The discussion remains open-ended, with various hypotheses and interpretations presented.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the relationships between gauge groups and compact manifolds, as well as the mathematical steps involved in deriving these connections. Some participants note that the gauge groups in string theory arise differently than in Kaluza-Klein theory, but the implications of these differences are not fully resolved.

  • #31
@Cyroos, I will be happy to continue working with you. But I have never been able to profit from my scientific interest.
 
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  • #32
I'll show U how to profit . . . ..
 
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  • #33
Cyroos said:
I'll show U how to profit . . . ..
Caution, @bayakiv -- This looks like a scam setup...
 
  • #34
@berkeman You needlessly worry about me. I work for an enterprise subject to US sanctions, so is it worth fearing fraud when faced with the banditry of one state in relation to another? By the way, commerce is quite appropriate here, you can, for example, sell a https://www.researchgate.net/publication/349426966_Vortex_Plasma_Thruster to an interested party.
 
Last edited:
  • #35
Dear Bayakiv !
i am no plotter / no scammer / no intriguer . ..
I just know how to put our in-common brand/branch of topology to best commercial use in Japan . . .
You decide for yourself to work with me in the long run OR not to . . .

Respect
Regards
Cyroos
 
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  • #36
Dear Cyross, I have no doubt about your honesty.
 
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  • #37
Thanx . .. . .. I have just arrived Japan
I only hope that my middle-man shall do a good job for us both . . .
I have NO experience of doing business , ,, ,,
 
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  • #38
Well this thread has taken an unexpected turn... :oldconfused:
 
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  • #39
wat's the problem , Eloheim ?
 
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  • #40
Thread closed for Moderation...
 
  • #41
Thread is closed after questionable user has been banned.

Cyroos said:
I'll show U how to profit . . . ..
Cyroos said:
Dear Bayakiv !
i am no plotter / no scammer / no intriguer . ..
I just know how to put our in-common brand/branch of topology to best commercial use in Japan . . .
You decide for yourself to work with me in the long run OR not to . . .

Respect
Regards
Cyroos
Cyroos said:
Thanx . .. . .. I have just arrived Japan
I only hope that my middle-man shall do a good job for us both . . .
I have NO experience of doing business , ,, ,,
 

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