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I've read that string theory is manifestly Lorentz invariant - however, I'm confused about this being true in 4D spacetime or in the full 10D setting of the theory (well, one version anyway). At some point I'd also read in a paper that 4D Lorentz invariance necessarily breaks Lorentz invariance in 10D ... however, I've misplaced the reference, unfortunately.

If Lorentz invariance in 10D is not satisfied, doesn't this have serious implications? (even if those dimensions are compactified) Or from a GR perspective, does one only care about the 4 extended spacetime dimensions?

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The conventional point of view is:

  • that the theory/action is generally covariant in 10D spacetime, and

  • that it is the vacuum state that breaks the symmetry down to 4D Poincare symmetry.

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  • $\begingroup$ Are there any implications for breaking the symmetry - e.g., without 10D Lorentz invariance, what happens to strings that occupy (in part) the extra 6 dimensions? I.e., what physical effects does this have? $\endgroup$ – asimo Jun 8 '17 at 10:35

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