Basic Ideas of Superstring Theory

A string's space-time history is described by functions Xm(s,t) which describe how the string's two-dimensional "world sheet," represented by coordinates (s,t), is mapped into space-time Xm. There are also functions defined on the two-dimensional world-sheet that describe other degrees of freedom, such as those associated with supersymmetry and gauge symmetries.
Surprisingly, classical string theory dynamics is described by a conformally invariant 2D quantum field theory. (Roughly, conformal invariance is symmetry under a change of length scale.) What distinguishes one-dimensional strings from higher dimensional analogs is the fact that this 2D theory is renormalizable (no bad short-distance infinities).
By contrast, objects with p dimensions, called "p-branes," have a (p+1)-dimensional world volume theory. For p > 1, those theories are non-renormalizable. This is the feature that gives strings a special status, even though, as we will discuss later, higher-dimensional p-branes do occur in superstring theory.

Perturbation Theory

Compactification of Extra Dimensions

A Theory of Everything?

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