Brane

A brane is an extended object in string theory and related theories, characterized by its number of spatial dimensions. Strings are one-dimensional branes; higher-dimensional examples include membranes.

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String theory: A framework in which fundamental excitations are one-dimensional strings rather than point particles. Branes extend the framework beyond its fundamental strings and provide additional physical objects.
Dirichlet boundary condition: A boundary condition that fixes a field or coordinate to a specified value at a boundary. Open-string endpoints obey this condition in directions transverse to a D-brane.
AdS/CFT correspondence: A conjectured equivalence between certain gravitational theories in anti-de Sitter space and conformal field theories on its boundary. Brane configurations helped motivate this duality and provide settings for studying it.
Fundamental string: A one-dimensional string regarded as a fundamental excitation of string theory. Unlike a D-brane, it is fundamental in perturbative string theory rather than defined by open-string endpoints.
Worldvolume: The spacetime swept out by an object as it evolves, with one dimension more than its spatial dimensions. A brane’s motion traces a worldvolume whose dimensionality encodes its spatial extent.
Nambu–Goto action: An action describing a relativistic string through the area of its worldsheet. Its brane generalizations describe dynamics using the volume swept out by an extended object.
Gauge/gravity duality: A proposed equivalence between a gauge theory and a gravitational theory in a higher-dimensional spacetime. Branes offer constructions in which gauge fields and gravity arise from different sectors.
NS5-brane: A five-dimensional brane magnetically charged under the Neveu–Schwarz two-form field. It is an NS-sector brane, contrasting with D-branes that carry Ramond–Ramond charge.
D-brane: A brane on which open strings can end, named for the Dirichlet boundary conditions imposed on those strings. D-branes are a well-studied class of branes that make the general idea concrete.
Dirac–Born–Infeld action: A nonlinear action governing gauge fields and embedding coordinates on a D-brane. It captures important low-energy dynamics of D-branes and their worldvolume fields.