further dimensions

Michael Green (interviewed by Davies and Brown in "Superstrings: a Theory of Everything?") says: "...The heterotic theories are rather curious beasts. ... (They combine) the string theory which works in twenty-six dimensional spacetime with one which works in twenty-six dimensions! That, of course, doesn't make sense. You can't have a different number of spacetime dimensions for the same string. What actually happens is that ten of the twenty-six dimensions are ordinary spacetime dimensions, so that the string is wriggling in ten-dimensional space-time. In addition there are sixteen so-called internal dimensions. These lead to extra structure in the theory that ought to describe the other forces, the forces other than gravity. So there's a rather geometrical picture for wherethese other forces come from. They come from the fact that twenty-six minus ten is sixteen! The sixteen mismatching dimensions are responsible for certain symmetries of the theory. These symmetries go under the names SO(32) and E8 x E8, which are mathematical names for the relationships between the particles in the theory. SO(32) and E8 x E8, are mathematical symmetry groups which are naturally associated, in the heterotic theory, with the mismatch of sixteen dimensions between the bosonic string theory and superstring theory."