Editing Mirror symmetry (string theory) (section)

===Strings and compactification===
{{main article|String theory|Compactification (physics)}}
[[Image:Open and closed strings.svg|right|thumb|alt=A wavy open segment and closed loop of string.|The fundamental objects of string theory are open and closed [[string (physics)|strings]]. ]]
In physics, [[string theory]] is a [[mathematical theory|theoretical framework]] in which the [[point particle|point-like particles]] of [[particle physics]] are replaced by one-dimensional objects called [[string (physics)|strings]]. These strings look like small segments or loops of ordinary string. String theory describes how strings propagate through space and interact with each other. On distance scales larger than the string scale, a string will look just like an ordinary particle, with its [[mass]], [[charge (physics)|charge]], and other properties determined by the vibrational state of the string. Splitting and recombination of strings correspond to particle emission and absorption, giving rise to the interactions between particles.<ref>For an accessible introduction to string theory, see {{harvnb|Greene|2000}}.</ref>

There are notable differences between the world described by string theory and the everyday world. In everyday life, there are three familiar dimensions of space (up/down, left/right, and forward/backward), and there is one dimension of time (later/earlier). Thus, in the language of modern physics, one says that [[spacetime]] is four-dimensional.<ref>{{harvnb|Wald|1984|page=4}}.</ref> One of the peculiar features of string theory is that it requires [[extra dimensions]] of spacetime for its mathematical consistency. In [[superstring theory]], the version of the theory that incorporates a theoretical idea called [[supersymmetry]], there are six extra dimensions of spacetime in addition to the four that are familiar from everyday experience.<ref>{{harvnb|Zwiebach|2009|page=8}}.</ref>

One of the goals of current research in string theory is to develop models in which the strings represent particles observed in high energy physics experiments. For such a model to be consistent with observations, its spacetime must be four-dimensional at the relevant distance scales, so one must look for ways to restrict the extra dimensions to smaller scales. In most realistic models of physics based on string theory, this is accomplished by a process called [[compactification (physics)|compactification]], in which the extra dimensions are assumed to "close up" on themselves to form circles.<ref name=autogenerated1>{{harvnb|Yau|Nadis|2010|loc=Ch. 6}}.</ref> In the limit where these curled up dimensions become very small, one obtains a theory in which spacetime has effectively a lower number of dimensions. A standard analogy for this is to consider a multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have only one dimension, its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling on the surface of the hose would move in two dimensions.<ref>This analogy is used for example in {{harvnb|Greene|2000|page=186}}.</ref>