T-Duality

The simplest, though one of the most far-reaching, dualities in string theory is “ -duality.” To get a sense of what this is, take a periodic interval of length , which you could alternatively think of as a circle. You could also consider a periodic version of square of side leading to a torus. Or a 3-dimensional version of this periodic box also known as a 3-dimensional torus. Imagine that this box is the universe and shrink . It gets smaller and smaller, and seemingly more compressed as in Fig. 83 .