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The Structure of the Extra Dimensions of String Theory

Final Report Summary - XD-STRING (The Structure of the Extra Dimensions of String Theory)

String theory is the idea that all particles are actually tiny vibrating strings. It was originally proposed to solve the problems that gravity and quantum mechanics seem to create if one admits that all particles are pointlike, and hence capable of getting arbitrarily close. The idea works extremely well, but only if one admits that spacetime has several spatial dimensions in addition to the three of our everyday experience. We do not see these dimensions in our everyday life or in experiments, but they might very well wrap a space so tiny as to have escaped detection so far. The goal of this Project was to understand the shape of this space. We wanted to characterize which possible shapes are allowed by the laws of string theory, and to what type of physics they would give rise.

These laws can be approximated well by "supergravity", a variant of Einstein's general relativity which also includes supersymmetry, a conjectural symmetry of the quantum world favored by string theory, that would relate matter and forces. The main tool we have used is a new formalism whose fundamental variables measure minimal volumes --- rather than distances, as originally done in general relativity.

We have obtained many new possible shapes for the extra dimensions, and several methods to look for many more, and to exclude many other possibilities which would mathematically look possible. We have also discovered new phenomena that occur when strings go close to "singularities", points where the shape is pinched and where the Einstein approximation does not work. Such results might point to new ways to realize in string theory the unification of forces, the idea suggested by current data that all elementary forces become in fact aspect of a single one at very short distances.