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Clarification question: 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?