Compactification of Extra Dimensions


As has already been mentioned, to have a chance of being realistic, the six extra space dimensions must curl up into a tiny geometrical space, whose size should be comparable to the string length Lst..
Since space-time geometry is determined dynamically (as in general relativity), only geometries that satisfy the dynamical equations are allowed.
The HE string theory, compactified on a particular kind of six-dimensional space, called a Calabi--Yau manifold, has many qualitative features at low energies that resemble the standard model. In particular, the low mass fermions (identified as quarks and leptons) occur in families, whose number is controlled by the topology of the CY manifold.
These successes have been achieved in a perturbative framework, and are necessarily qualitative at best, since non-perturbative phenomena are essential to an understanding of supersymmetry breaking and other important matters of detail.


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| Contents | Resolving Contradictions | Supersymmetry | A Brief History of Superstings |

| Basic Ideas of Superstring Theory | Superstring Revolution, part deux |