Editing M-theory (section)

===Relationships between string theories===

Although there were only a handful of consistent superstring theories, it remained a mystery why there was not just one consistent formulation.<ref name="Duff 1998, p. 65"/> However, as physicists began to examine string theory more closely, they realized that these theories are related in intricate and nontrivial ways.<ref>Duff 1998</ref>

In the late 1970s, Claus Montonen and [[David Olive]] had conjectured a special property of certain physical theories.<ref>Montonen and Olive 1977</ref> A sharpened version of their conjecture concerns a theory called [[N = 4 supersymmetric Yang–Mills theory|{{math|''N'' {{=}} 4}} supersymmetric Yang–Mills theory]], which describes theoretical particles formally similar to the [[quark]]s and [[gluon]]s that make up [[atomic nucleus|atomic nuclei]]. The strength with which the particles of this theory interact is measured by a number called the [[coupling constant]]. The result of Montonen and Olive, now known as [[Montonen–Olive duality]], states that {{math|''N'' {{=}} 4}} supersymmetric Yang–Mills theory with coupling constant {{math|''g''}} is equivalent to the same theory with coupling constant {{math|1/''g''}}. In other words, a system of strongly interacting particles (large coupling constant) has an equivalent description as a system of weakly interacting particles (small coupling constant) and vice versa<ref name="Duff 1998, p. 66">Duff 1998, p. 66</ref> by spin-moment.

In the 1990s, several theorists generalized Montonen–Olive duality to the S-duality relationship, which connects different string theories. [[Ashoke Sen]] studied S-duality in the context of heterotic strings in four dimensions.<ref>Sen 1994a</ref><ref>Sen 1994b</ref> [[Chris Hull]] and [[Paul Townsend]] showed that type IIB string theory with a large coupling constant is equivalent via S-duality to the same theory with small coupling constant.<ref>Hull and Townsend 1995</ref> Theorists also found that different string theories may be related by T-duality. This duality implies that strings propagating on completely different spacetime geometries may be physically equivalent.<ref name="Duff 1998, p. 67">Duff 1998, p. 67</ref>