Editing M-theory (section)

===Dualities===

{{main article|String duality|S-duality|T-duality}}

[[File:StringTheoryDualities.svg|right|thumb|alt=A diagram indicating the relationships between M-theory and the five string theories.|upright=1.2|A diagram of string theory dualities. Yellow arrows indicate [[S-duality]]. Blue arrows indicate [[T-duality]]. These dualities may be combined to obtain equivalences of any of the five theories with M-theory.<ref>Becker, Becker, and Schwarz 2007, pp. 339–347</ref>]]

Theories that arise as different limits of M-theory turn out to be related in highly nontrivial ways. One of the relationships that can exist between these different physical theories is called [[S-duality]]. This is a relationship which says that a collection of strongly interacting particles in one theory can, in some cases, be viewed as a collection of weakly interacting particles in a completely different theory. Roughly speaking, a collection of particles is said to be strongly interacting if they combine and decay often and weakly interacting if they do so infrequently. [[Type I string theory]] turns out to be equivalent by S-duality to the {{math|''SO''(32)}} heterotic string theory. Similarly, [[type IIB string theory]] is related to itself in a nontrivial way by S-duality.<ref name="Becker, Becker, and Schwarz 2007">Becker, Becker, and Schwarz 2007</ref>

Another relationship between different string theories is [[T-duality]]. Here one considers strings propagating around a circular extra dimension. T-duality states that a string propagating around a circle of radius {{math|''R''}} is equivalent to a string propagating around a circle of radius {{math|1/''R''}} in the sense that all observable quantities in one description are identified with quantities in the dual description. For example, a string has [[momentum]] as it propagates around a circle, and it can also wind around the circle one or more times. The number of times the string winds around a circle is called the [[winding number]]. If a string has momentum {{math|''p''}} and winding number {{math|''n''}} in one description, it will have momentum {{math|''n''}} and winding number {{math|''p''}} in the dual description. For example, [[type IIA string theory]] is equivalent to type IIB string theory via T-duality, and the two versions of heterotic string theory are also related by T-duality.<ref name="Becker, Becker, and Schwarz 2007"/>

In general, the term ''[[string duality|duality]]'' refers to a situation where two seemingly different [[physical system]]s turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory. The two theories are then said to be ''dual'' to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.<ref>Zwiebach 2009, p. 376</ref>