Editing M-theory (section)

==Phenomenology==

===Overview===

{{main article|String phenomenology}}

[[Image:Calabi yau formatted.svg|right|thumb|alt=Visualization of a complex mathematical surface with many convolutions and self intersections.|A cross section of a [[Calabi–Yau manifold]] ]]

In addition to being an idea of considerable theoretical interest, M-theory provides a framework for constructing models of real world physics that combine general relativity with the [[standard model of particle physics]]. [[Phenomenology (particle physics)|Phenomenology]] is the branch of theoretical physics in which physicists construct realistic models of nature from more abstract theoretical ideas. [[String phenomenology]] is the part of string theory that attempts to construct realistic models of particle physics based on string and M-theory.<ref>Dine 2000</ref>

Typically, such models are based on the idea of compactification.{{efn|[[Brane world]] scenarios provide an alternative way of recovering real world physics from string theory. See Randall and Sundrum 1999.}} Starting with the ten- or eleven-dimensional spacetime of string or M-theory, physicists postulate a shape for the extra dimensions. By choosing this shape appropriately, they can construct models roughly similar to the standard model of particle physics, together with additional undiscovered particles,<ref>Candelas et al. 1985</ref> usually [[supersymmetry|supersymmetric]] partners to analogues of known particles. One popular way of deriving realistic physics from string theory is to start with the heterotic theory in ten dimensions and assume that the six extra dimensions of spacetime are shaped like a six-dimensional [[Calabi–Yau manifold]]. This is a special kind of geometric object named after mathematicians [[Eugenio Calabi]] and [[Shing-Tung Yau]].<ref>Yau and Nadis 2010, p. ix</ref> Calabi–Yau manifolds offer many ways of extracting realistic physics from string theory. Other similar methods can be used to construct models with physics resembling to some extent that of our four-dimensional world based on M-theory.<ref>Yau and Nadis 2010, pp. 147–150</ref>

Partly because of theoretical and mathematical difficulties and partly because of the extremely high energies (beyond what is technologically possible for the foreseeable future) needed to test these theories experimentally, there is so far no experimental evidence that would unambiguously point to any of these models being a correct fundamental description of nature. This has led some in the community to criticize these approaches to unification and question the value of continued research on these problems.<ref>Woit 2006</ref>

===Compactification on {{math|''G''<sub>2</sub>}} manifolds===

In one approach to M-theory phenomenology, theorists assume that the seven extra dimensions of M-theory are shaped like a [[G2 manifold|{{math|''G''<sub>2</sub>}} manifold]]. This is a special kind of seven-dimensional shape constructed by mathematician [[Dominic Joyce]] of the [[University of Oxford]].<ref>Yau and Nadis 2010, p. 149</ref> These {{math|''G''<sub>2</sub>}} manifolds are still poorly understood mathematically, and this fact has made it difficult for physicists to fully develop this approach to phenomenology.<ref name="Yau and Nadis 2010, p. 150">Yau and Nadis 2010, p. 150</ref>

For example, physicists and mathematicians often assume that space has a mathematical property called [[smooth manifold|smoothness]], but this property cannot be assumed in the case of a {{math|''G''<sub>2</sub>}} manifold if one wishes to recover the physics of our four-dimensional world. Another problem is that {{math|''G''<sub>2</sub>}} manifolds are not [[complex manifold]]s, so theorists are unable to use tools from the branch of mathematics known as [[complex analysis]]. Finally, there are many open questions about the existence, uniqueness, and other mathematical properties of {{math|''G''<sub>2</sub>}} manifolds, and mathematicians lack a systematic way of searching for these manifolds.<ref name="Yau and Nadis 2010, p. 150"/>

===Heterotic M-theory===

Because of the difficulties with {{math|''G''<sub>2</sub>}} manifolds, most attempts to construct realistic theories of physics based on M-theory have taken a more indirect approach to compactifying eleven-dimensional spacetime. One approach, pioneered by Witten, Hořava, [[Burt Ovrut]], and others, is known as heterotic M-theory. In this approach, one imagines that one of the eleven dimensions of M-theory is shaped like a circle. If this circle is very small, then the spacetime becomes effectively ten-dimensional. One then assumes that six of the ten dimensions form a Calabi–Yau manifold. If this Calabi–Yau manifold is also taken to be small, one is left with a theory in four-dimensions.<ref name="Yau and Nadis 2010, p. 150"/>

Heterotic M-theory has been used to construct models of [[brane cosmology]] in which the observable universe is thought to exist on a brane in a higher dimensional ambient space. It has also spawned alternative theories of the early universe that do not rely on the theory of [[cosmic inflation]].<ref name="Yau and Nadis 2010, p. 150"/>