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There is an aspect of String Theory I am not clear on: the higher-dimensional background geometry. Is it flat or curved? If it is curved, then what describes or accounts for the back-reaction of the strings and branes to the background? If there is back-reaction to the higher-dimensional background geometry, then is it also a process that is to be quantized and, if so, how? (At this point, you may add a comment "Oh, I see what you did with the title there!" [chuckle, chuckle]). Was this the role that Supergravity was to play, in String Theory? And has Supergravity been integrated with String Theory, if so?

I assume there is a whole range of versions of string theory out there that answer each of the aspects of the issue of the background, that I laid out, differently. I'm not familiar with the landscape.

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    $\begingroup$ If the higher dimensions were flat, wouldn’t we have noticed them? $\endgroup$ Commented Sep 29, 2024 at 20:58
  • $\begingroup$ The whole point of compactified dimensions is that they are compactified, i.e. are closed/periodic/insignificant at large scales, often described as "tightly rolled up". This constitutes a great deal of curvature, to Ghoster's point. $\endgroup$ Commented Sep 29, 2024 at 21:07
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    $\begingroup$ Has Supergravity been integrated with String Theory? See en.wikipedia.org/wiki/Supergravity#Relation_to_superstrings $\endgroup$ Commented Sep 29, 2024 at 21:27
  • $\begingroup$ A circle is flat, however tiny you take it to be. Similarly, by taking the Cartesian produces of tiny circles, you get flat toruses of arbitrary dimension, as small as you like. $\endgroup$ Commented Sep 29, 2024 at 21:42
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    $\begingroup$ I don’t think string theory can repro low-energy phenomenology if the extra dimensions are a flat torus. Isn’t that why string theorists were led to consider Calabi-Yau spaces? $\endgroup$ Commented Sep 29, 2024 at 21:57

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