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String theory
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=== Unification of superstring theories === [[File:Limits of M-theory.svg|upright=1.6|thumb|alt=A star-shaped diagram with the various limits of M-theory labeled at its six vertices.|A schematic illustration of the relationship between [[M-theory]], the five [[superstring theory|superstring theories]], and eleven-dimensional [[supergravity]]. The shaded region represents a family of different physical scenarios that are possible in M-theory. In certain limiting cases corresponding to the cusps, it is natural to describe the physics using one of the six theories labeled there.]] In the 1970s, many physicists became interested in [[supergravity]] theories, which combine general relativity with supersymmetry. Whereas general relativity makes sense in any number of dimensions, supergravity places an upper limit on the number of dimensions.<ref>[[#Duff1998|Duff]], p. 64</ref> In 1978, work by [[Werner Nahm]] showed that the maximum spacetime dimension in which one can formulate a consistent supersymmetric theory is eleven.<ref name=Nahm/> In the same year, [[Eugene Cremmer]], [[Bernard Julia]], and [[Joël Scherk]] of the [[École Normale Supérieure]] showed that supergravity not only permits up to eleven dimensions but is in fact most elegant in this maximal number of dimensions.<ref name=Cremmer/><ref name="Duff 1998, p. 65">[[#Duff1998|Duff]], p. 65</ref> Initially, many physicists hoped that by compactifying [[eleven-dimensional supergravity]], it might be possible to construct realistic models of our four-dimensional world. The hope was that such models would provide a unified description of the four fundamental forces of nature: electromagnetism, the [[strong nuclear force|strong]] and [[weak nuclear force]]s, and gravity. Interest in eleven-dimensional supergravity soon waned as various flaws in this scheme were discovered. One of the problems was that the laws of physics appear to distinguish between clockwise and counterclockwise, a phenomenon known as [[chirality (physics)|chirality]]. Edward Witten and others observed this chirality property cannot be readily derived by compactifying from eleven dimensions.<ref name="Duff 1998, p. 65"/> In the [[first superstring revolution]] in 1984, many physicists turned to string theory as a unified theory of particle physics and quantum gravity. Unlike supergravity theory, string theory was able to accommodate the chirality of the standard model, and it provided a theory of gravity consistent with quantum effects.<ref name="Duff 1998, p. 65"/> Another feature of string theory that many physicists were drawn to in the 1980s and 1990s was its high degree of uniqueness. In ordinary particle theories, one can consider any collection of elementary particles whose classical behavior is described by an arbitrary [[Lagrangian (field theory)|Lagrangian]]. In string theory, the possibilities are much more constrained: by the 1990s, physicists had argued that there were only five consistent supersymmetric versions of the theory.<ref name="Duff 1998, p. 65"/> 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. They found that a system of strongly interacting strings can, in some cases, be viewed as a system of weakly interacting strings. This phenomenon is known as S-duality. It was studied by Ashoke Sen in the context of heterotic strings in four dimensions<ref name=Sen1994a/><ref name=Sen1994b/> and by Chris Hull and Paul Townsend in the context of the type IIB theory.<ref name=Hull/> 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>[[#Duff1998|Duff]], p. 67</ref> At around the same time, as many physicists were studying the properties of strings, a small group of physicists were examining the possible applications of higher dimensional objects. In 1987, Eric Bergshoeff, Ergin Sezgin, and Paul Townsend showed that eleven-dimensional supergravity includes two-dimensional branes.<ref name=Bergshoeff/> 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 name=Duff1987/> 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. Duff and his collaborators showed that this construction reproduces exactly the strings appearing in type IIA superstring theory.<ref>[[#Duff1998|Duff]], p. 66</ref> Speaking at a string theory conference in 1995, Edward Witten made the surprising suggestion that all five superstring theories were in fact just different limiting cases of a single theory in eleven spacetime dimensions. Witten's announcement drew together all of the previous results on S- and T-duality and the appearance of higher-dimensional branes in string theory.<ref name=Witten1995/> In the months following Witten's announcement, hundreds of new papers appeared on the Internet confirming different parts of his proposal.<ref>[[#Duff1998|Duff]], pp. 67–68</ref> Today this flurry of work is known as the second superstring revolution.<ref>[[#Becker|Becker, Becker and Schwarz]], p. 296</ref> Initially, some physicists suggested that the new theory was a fundamental theory of membranes, but Witten was skeptical of the role of membranes in the theory. In a paper from 1996, Hořava and Witten wrote "As it has been proposed that the eleven-dimensional theory is a supermembrane theory but there are some reasons to doubt that interpretation, we will non-committally call it the M-theory, leaving to the future the relation of M to membranes."<ref name=Horava/> In the absence of an understanding of the true meaning and structure of M-theory, Witten has suggested that the ''M'' should stand for "magic", "mystery", or "membrane" according to taste, and the true meaning of the title should be decided when a more fundamental formulation of the theory is known.<ref name=Duff1996/>
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