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The five super-string theories are generally said to be 10-dimensional. However the Heterotic theories combine a bosonic left mover (which lives in 26 dimensions) with a super right mover (which lives in 10 dimensions). The extra 16 dimensions compactify into a torus with either $\frac{\operatorname{Spin}32}{\mathbb Z_ 2}$ or $E_8\times E_8$ symmetry.

So these theories differ from the others by this compact torus.

What is the effect of the this torus physically?

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You mean extra 16? – Prahar Jun 22 '13 at 1:47
    
Simply, it gives the string theories different gauge groups (so clearly, different physical meaning, even though the actions are the same, heterotic action) – centralcharge Jun 22 '13 at 4:42
    
@prahar:yes - obviously forgotten arithmetic. – Mozibur Ullah Jun 22 '13 at 11:52

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