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In special relativity there is a clear difference between spatial and temporal dimensions of spacetime due to the Minkowski metric diag(-1,1,1,1). In higher dimensional theories (10- and 26-dimensional string theories) does this asymmetry continue with additional dimensions being specifically time- or space-like or is there no clear difference?

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From Polchinski's String Theory, Chapter 1:

We want to study the classical and quantum dynamics of a one-dimensional object, a string. The string moves in $D$ flat spacetime dimensions, with metric $\eta_{\mu \nu} = \mathrm{diag}(-,+,+,\cdots,+)$.

So all additional dimensions are spacelike.

Strictly speaking Polchinski is only talking about bosonic string theory at this point, but I believe the same applies to superstring theories as well. (It's been a long time since I thought about this in any detail.)

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  • $\begingroup$ This tells us that the answer is X, but it doesn't tell us why the answer is X. $\endgroup$ – user4552 Jul 29 '19 at 19:30
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    $\begingroup$ @BenCrowell: Nor did the question ask why the answer was X. ;-) $\endgroup$ – Michael Seifert Jul 29 '19 at 19:31
  • $\begingroup$ This answer also suggests that the answer is not necessarily what you claim: physics.stackexchange.com/a/43637/4552 . The only way to clear this up and learn something would be to understand the whys, rather than just quoting Aristotle as an authority. $\endgroup$ – user4552 Jul 29 '19 at 19:39
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    $\begingroup$ @BenCrowell: That's a fair perspective, and if someone wants to write an answer explaining the whys, I'll happily upvote it. Mainly I wanted to ensure that the question didn't go unanswered, since the question seemed to be asking for a specific answer in the context of string theory. $\endgroup$ – Michael Seifert Jul 29 '19 at 19:50

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