Reading popular accounts on string theory, I have the impression that the number of extra dimensions of string theory is not an ad hoc postulate; it's uniquely determined by mathematical consistency.

On the other hand, the primitive Kaluza-Klein theory and Randall-Sundrum model of warped extra dimension were originally 5D theories; the existence of just one extra dimension seems to be an ad hoc postulate. Are there decent motivations for only one extra dimensions other than simplifying the theory?

  • $\begingroup$ I hope a theorist addresses this. AFAIK Kaluza-Klein was the first attempt at unifying electromagnetism and gravity mathematically. No space for the standard model. The Randall-Sundrum is modelling the standard model and gravity, with massive gravitons, and standard model particles, and it seems compettitive to string theories. It has not been falsified afaik. String theories model the particles as excitations of a fundamental string ( instead of point particles) , a different logic, close to the kaluza-klein logic. $\endgroup$ – anna v May 6 '18 at 13:29
  • $\begingroup$ RS is consistent, not competitive, with string theory. Also, no massive gravity. $\endgroup$ – bapowell May 6 '18 at 14:15
  • $\begingroup$ @bapowell how about this indico.cern.ch/event/129980/contributions/1350939/attachments/… $\endgroup$ – anna v May 6 '18 at 14:31
  • $\begingroup$ Thanks for the link! What are you showing me here? $\endgroup$ – bapowell May 6 '18 at 15:27
  • $\begingroup$ I see: there are massive gravitons as KK excitation. I stand corrected, thank you. $\endgroup$ – bapowell May 6 '18 at 15:35

Kaluza-Klein is looking to unify gravity and electromagnetism, for which only a single extra dimension is needed. Randall-Sundrum meanwhile is a model attempting to explain the relative weakness of gravity, and so contains a 5th “large” extra dimension that runs perpendicular to the brane. The idea is that gravity “leaks” off the 4D brane into this so-called “bulk”. Their setup is entirely consistent with additional compactified dimensions, but they’re not discussed because they’re not relevant to the novel mechanism of the model.

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