Does the poincare conjecture disprove the shape of strings in string theory

  • #1
Considering that the smallest particles in nature are supposed to be strings, which are donut and line shapes. And the poincare conjecture says the simplest shape in nature is a sphere. wouldn't it make sense that the true fundamental particles are sphere shaped and that if they combine to form other shapes, it is from some other property of nature.
 
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  • #2
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Considering that the smallest particles in nature are supposed to be strings, which are donut and line shapes. And the poincare conjecture says the simplest shape in nature is a sphere. wouldn't it make sense that the true fundamental particles are sphere shaped and that if they combine to form other shapes, it is from some other property of nature.
Not some other property of nature, per se, necessarily, but that there had been a considerable amount of activity by the time the doughnut or line shape entities emerged. String theory, as any fundamental theory, has to start from somewhere. Are the fundamental entities of string theory a product of a fundamental wave dynamic that might be connected to, say, the Poincare conjecture and the Huygens-Fresnel principle?
 
  • #3
604
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How could the poincaré conjecture possibly disprove string theory?
To start off with, there's no way any theorem from pure mathematics could ever prove or disprove the applicability of any theory based on correct mathematics to the real world.
Secondly, it doesn't say that the simplest shape in nature is a sphere. It says that any simply connected 3-manifold is homeomorphic to the 3-sphere.
Thirdly, strings aren't 3-dimensional objects, and their two-dimensional worldsheets aren't simply connected at anything other than the first order in perturbation theory, so it seems to me to be a fairly unlikely candidate to have anything to do with some more fundamental physics.
Fourthly, and we're now onto topics that I don't claim to understand at all, but I'm aware that there's a connection between the mathematical techniques Perelman used to prove the conjecture and certain features of RG running and the dilaton in string theory. I don't understand this point at all, although David Tong seems to- see section 7 of his lecture notes.

If there's a productive conversation to be had here, it might also be more likely to be had in the 'beyond the standard model' forum rather than this one.
 

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