Both T-duality and S-duality relate different string theories together. String theory skeptics aren’t convinced that these dualities in some specific states of the theories relate to a more fundamental duality of the theories at all levels. Here’s a review of the existing string theory relationships:

  • Type I and Type HO superstring theories are related by S-duality.

  • Type HO and Type HE superstring theories are related by T-duality.

  • Type IIA and Type IIB superstring theories are related by T-duality.

With these dualities (and other, more subtle ones, which relate IIA and IIB together with the heterotic string theories), relationships exist to transform one version of string theory into another one — at least for certain specially selected string theory conditions.

To solve these equations of duality, certain assumptions have to be made, and not all of them are necessarily valid in a string theory that would describe our own universe. For example, the theories can only be proved in cases of perfect supersymmetry, while our own universe exhibits (at best) broken supersymmetry.

Physicist (and string theory skeptic) Lee Smolin calls the belief that these dualities do not represent duality at all levels of the theory the pessimistic view, while calling the string theory belief in the fundamental nature of these dualities the optimistic view.

Still, in 1995 it was hard not to be in the optimistic camp (and, in fact, many had never stopped being optimistic about string theory). The very fact that these dualities existed at all was startling to string theorists.

It wasn’t planned, but came out of the mathematical analysis of the theory. This was seen as powerful evidence that string theory was on the right track. Instead of falling apart into a bunch of different theories, superstring theory was actually pulling back together into one single theory — Edward Witten’s M-theory — which manifested itself in a variety of ways.