Brane

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For other uses, see Brane (disambiguation).

In theoretical physics, a brane is a physical object that generalizes the notion of a point particle to higher dimensions.[1] For example, 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 "membrane", which is equivalent to a two-dimensional brane.

Branes are dynamic objects that 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 fields analogous to the electromagnetic field that couple to the worldvolume of a brane.

In string theory and related theories, D-branes 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 the fact that we impose a certain mathematical condition on the system known as the Dirichlet boundary condition. The study of D-branes has led to important results, such as the anti-de Sitter/conformal field theory correspondence, which has shed light on many problems in quantum field theory.

Branes are also frequently studied from a purely mathematical point of view, since they are related to subjects such as homological mirror symmetry and noncommutative geometry.[2] Mathematically, branes may be represented as objects of certain categories, such as the derived category of coherent sheaves on a Calabi–Yau manifold, or the Fukaya category.

Supermembrane[edit]

The membrane found in 11 dimensional M-Theory and supergravity is the supermembrane. This is a supersymmetric brane and is anomaly free in 11 dimensions only.

See also[edit]

References[edit]

  1. ^ Moore, Gregory (2005). "What is... a Brane?" (PDF). Notices of the AMS 52: 214. Retrieved June 2013. 
  2. ^ Aspinwall, Paul; Bridgeland, Tom; Craw, Alastair; Douglas, Michael; Gross, Mark; Kapustin, Anton; Moore, Gregory; Segal, Graeme; Szendröi, Balázs; Wilson, P.M.H., eds. (2009). Dirichlet Branes and Mirror Symmetry. American Mathematical Society.