# Are every consistent String theories compactification of 10D strings?

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It's known that there are only five consistent tachyonless spacetime-supersymmetric string theories with non-compact ten dimensions, and one more tachyonless ten-dimensional string theory with non-compact ten dimensions that is not supersymmetric ($SO(16)\times SO(16)$ heterotic string). Is any consistent string theory without tachyons in lower dimensions a compactification of any of these? There are known string theories in lower dimensions that is not known how to embebed or is known that can't be embebed as a compactification of their ten-dimensional cousins?

Background: I had read Polchinsky Vol 1 and from Vol 2 the chapters 10, 11, 12, 13 and parts of chapter 14. I hadn't done all the exercises from that.

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