We have so far failed to mention one of the biggest developments in string theory, yet another duality, this one very general. It is usually called the holographic duality, or the holographic principle. The holographic principle is not just a property of string theories, but also a supposed property of any useful theory of quantum gravity. The basic idea is that the description of a volume of space (d) can be thought of as encoded on a lower-dimensional boundary (d - 1) of the region. First proposed by Gerard 't Hooft, it was given a precise string theoretic interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Leonard Susskind said, “The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional surface.” As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of such holography is the famous AdS/CFT correspondence, which we have already briefly mentioned, but the formal holographic duality is much more general in scope. [Text largely from Wikipedia] The idea has obvious applications to quantum gravity.

Gerard 't Hooft

Leonard Susskind

This whole topic is currently the focus of extremely intense current research, and I am not competent to summarize it even in the vaguest possible way. There is a weekly seminar on the topic right here at UT physics.  Currently there exists no formal proof of this general duality, just as there exists no formal proof of a special case, the famous AdS/CFT duality.