Editing M-theory (section)

===Membranes and fivebranes===

String theory extends ordinary particle physics by replacing zero-dimensional point particles by one-dimensional objects called strings. In the late 1980s, it was natural for theorists to attempt to formulate other extensions in which particles are replaced by two-dimensional [[supermembranes]] or by higher-dimensional objects called branes. Such objects had been considered as early as 1962 by [[Paul Dirac]],<ref>Dirac 1962</ref> and they were reconsidered by a small but enthusiastic group of physicists in the 1980s.<ref name="Duff 1998, p. 65"/>

Supersymmetry severely restricts the possible number of dimensions of a brane. In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes.<ref>Bergshoeff, Sezgin, and Townsend 1987</ref> Intuitively, these objects look like sheets or membranes propagating through the eleven-dimensional spacetime. Shortly after this discovery, [[Michael Duff (physicist)|Michael Duff]], Paul Howe, Takeo Inami, and Kellogg Stelle considered a particular compactification of eleven-dimensional supergravity with one of the dimensions curled up into a circle.<ref>Duff et al. 1987</ref> In this setting, one can imagine the membrane wrapping around the circular dimension. If the radius of the circle is sufficiently small, then this membrane looks just like a string in ten-dimensional spacetime. In fact, Duff and his collaborators showed that this construction reproduces exactly the strings appearing in type IIA superstring theory.<ref name="Duff 1998, p. 66"/>

In 1990, [[Andrew Strominger]] published a similar result which suggested that strongly interacting strings in ten dimensions might have an equivalent description in terms of weakly interacting five-dimensional branes.<ref>Strominger 1990</ref> Initially, physicists were unable to prove this relationship for two important reasons. On the one hand, the Montonen–Olive duality was still unproven, and so Strominger's conjecture was even more tenuous. On the other hand, there were many technical issues related to the quantum properties of five-dimensional branes.<ref>Duff 1998, pp. 66–67</ref> The first of these problems was solved in 1993 when [[Ashoke Sen]] established that certain physical theories require the existence of objects with both [[electric charge|electric]] and [[magnetic monopole|magnetic]] charge which were predicted by the work of Montonen and Olive.<ref>Sen 1993</ref>

In spite of this progress, the relationship between strings and five-dimensional branes remained conjectural because theorists were unable to quantize the branes. Starting in 1991, a team of researchers including Michael Duff, Ramzi Khuri, Jianxin Lu, and Ruben Minasian considered a special compactification of string theory in which four of the ten dimensions curl up. If one considers a five-dimensional brane wrapped around these extra dimensions, then the brane looks just like a one-dimensional string. In this way, the conjectured relationship between strings and branes was reduced to a relationship between strings and strings, and the latter could be tested using already established theoretical techniques.<ref name="Duff 1998, p. 67"/>