David Corfield
mathematical landscape


The is a network of rich, interesting mathematical structures. These are often associated with physical theories, in particular arising from M-theoretic and string theoretic compactifications and dualities.

Exceptional structures are often found here. See universal exceptionalism.


1.3 Dualities of Compactified Theories

Since we have seen that the full string theories are all interrelated by a sequence of dualities, one would expect that their compactifications are also related by dualities. As it turns out, these relations are so abundant that we can make the following observation:

“Conjecture”: Whenever the dimension, number of preserved supercharges, and chiralities of two different compactifications of string theory match, there are choices of compactification geometries such that they are dual descriptions of the same physical theory.

Surprisingly, we are aware of no known counter examples. In this sense, dualities in lower dimensional theories are not hard to find, but rather are hard to prevent! One rationale for the existence of dualities is as Sergio Cecotti puts it, “the scarcity of rich structures”. In particular the very existence of quantum systems of gravity is hard to arrange and if we succeed to get more than one theory with a given symmetry, there is a good chance we have landed on the same theory. (The String Landscape, the Swampland, and the Missing Corner, arXiv: 1711.00864, p. 7)

Last revised on January 2, 2020 at 11:11:27. See the history of this page for a list of all contributions to it.