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String theory
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=== Matrix theory === {{main|Matrix theory (physics)}} In mathematics, a [[matrix (mathematics)|matrix]] is a rectangular array of numbers or other data. In physics, a [[matrix theory (physics)|matrix model]] is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way. A matrix model describes the behavior of a set of matrices within the framework of quantum mechanics.<ref name=Banks/> One important example of a matrix model is the BFSS matrix model proposed by [[Tom Banks (physicist)|Tom Banks]], [[Willy Fischler]], [[Stephen Shenker]], and [[Leonard Susskind]] in 1997. This theory describes the behavior of a set of nine large matrices. In their original paper, these authors showed, among other things, that the low energy limit of this matrix model is described by eleven-dimensional supergravity. These calculations led them to propose that the BFSS matrix model is exactly equivalent to M-theory. The BFSS matrix model can therefore be used as a prototype for a correct formulation of M-theory and a tool for investigating the properties of M-theory in a relatively simple setting.<ref name=Banks/> The development of the matrix model formulation of M-theory has led physicists to consider various connections between string theory and a branch of mathematics called [[noncommutative geometry]]. This subject is a generalization of ordinary geometry in which mathematicians define new geometric notions using tools from [[noncommutative algebra]].<ref name=Connes/> In a paper from 1998, [[Alain Connes]], [[Michael R. Douglas]], and [[Albert Schwarz]] showed that some aspects of matrix models and M-theory are described by a [[noncommutative quantum field theory]], a special kind of physical theory in which spacetime is described mathematically using noncommutative geometry.<ref name=CDS/> This established a link between matrix models and M-theory on the one hand, and noncommutative geometry on the other hand. It quickly led to the discovery of other important links between noncommutative geometry and various physical theories.<ref name=Nekrasov/><ref name=SW/>
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