Editing String theory (section)

=== Branes ===
{{main|Brane}}
[[File:D3-brane et D2-brane.PNG|thumb|right|alt=A pair of surfaces joined by wavy line segments.|Open strings attached to a pair of [[D-brane]]s]]

In string theory and other related theories, a [[brane]] is a physical object that generalizes the notion of a point particle to higher dimensions. For instance, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one. It is also possible to consider higher-dimensional branes. In dimension ''p'', these are called ''p''-branes. The word brane comes from the word "membrane" which refers to a two-dimensional brane.<ref name="Moore 2005, p. 214"/>

Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. A ''p''-brane sweeps out a (''p''+1)-dimensional volume in spacetime called its ''worldvolume''. Physicists often study [[field (physics)|fields]] analogous to the electromagnetic field which live on the worldvolume of a brane.<ref name="Moore 2005, p. 214"/>

In string theory, [[D-brane]]s are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to a certain mathematical condition on the system known as the [[Dirichlet boundary condition]]. The study of D-branes in string theory has led to important results such as the AdS/CFT correspondence, which has shed light on many problems in quantum field theory.<ref name="Moore 2005, p. 214"/>

Branes are frequently studied from a purely mathematical point of view, and they are described as objects of certain [[category (mathematics)|categories]], such as the [[derived category]] of [[coherent sheaf|coherent sheaves]] on a [[complex algebraic variety]], or the [[Fukaya category]] of a [[symplectic manifold]].<ref name="Aspinwall et al. 2009"/> The connection between the physical notion of a brane and the mathematical notion of a category has led to important mathematical insights in the fields of [[algebraic geometry|algebraic]] and [[symplectic geometry]]<ref name="Kontsevich 1995"/> and [[representation theory]].<ref name=Kapustin/>