D-branes are typically classified by their spatial dimension, which is indicated by a number written after the D. A D0-brane is a single point, a D1-brane is a line (sometimes called a "D-string"), a D2-brane is a plane, and a D25-brane fills the highest-dimensional space considered in bosonic string theory.
D-branes were discovered by Jin Dai, Robert Leigh, and Joseph Polchinski,[1] and independently by Petr Hořava,[2] in 1989.
In 1995, Polchinski identified D-branes with black p-brane solutions of supergravity, a discovery that triggered the second superstring revolution and led to both holographic and M-theory dualities.
If p spatial dimensions satisfy the Neumann boundary condition, then the string endpoint is confined to move within a p-dimensional hyperplane.
More generally, the branes are described by non-commutative geometry, which allows exotic behavior such as the Myers effect, in which a collection of Dp-branes expand into a D(p+2)-brane.
Ashoke Sen has argued that in Type IIB string theory, tachyon condensation allows (in the absence of Neveu-Schwarz 3-form flux) an arbitrary D-brane configuration to be obtained from a stack of D9 and anti D9-branes.
This is due to the lack of an exact string field theory that would describe the off-shell evolution of the tachyon.
Material objects, made of open strings, are bound to the D-brane, and cannot move "at right angles to reality" to explore the Universe outside the brane.
Because closed strings do not have to be attached to D-branes, gravitational effects could depend upon the extra dimensions orthogonal to the brane.
The annulus amplitude yields singularities that correspond to the on-shell production of open strings stretched between the two branes.
At non-relativistic scattering velocities the open strings may be described by a low-energy effective action that contains two complex scalar fields that are coupled via a term
If a Dp-brane is embedded in a spacetime of d spatial dimensions, the brane carries (in addition to its Maxwell field) a set of d − p massless scalars (particles which do not have polarizations like the photons making up light).
In fact, these massless scalars are Goldstone excitations of the brane, corresponding to the different ways the symmetry of empty space can be broken.
D-branes can be used to generate gauge theories of higher order, in the following way: Consider a group of N separate Dp-branes, arranged in parallel for simplicity.
The zero-mass states in the open-string particle spectrum for a system of N coincident D-branes yields a set of interacting quantum fields which is exactly a U(N) gauge theory.
Gauge theories were not invented starting with bosonic or fermionic strings; they originated from a different area of physics, and have become quite useful in their own right.
In order to maintain the second law of thermodynamics, one must postulate that the black hole gained whatever entropy the infalling gas originally had.
In an ordinary situation, a system has entropy when a large number of different "microstates" can satisfy the same macroscopic condition.
This model gives rough agreement with the expected entropy of a Schwarzschild black hole, but an exact proof has yet to be found one way or the other.
The chief difficulty is that it is relatively easy to count the degrees of freedom quantum strings possess if they do not interact with one another.
Therefore, calculating black hole entropy requires working in a regime where string interactions exist.
Extending the simpler case of non-interacting strings to the regime where a black hole could exist requires supersymmetry.
The challenge for a string theorist is to devise a situation in which a black hole can exist which does not "break" supersymmetry.
A series of 1975–76 papers by Bardeen, Bars, Hanson and Peccei dealt with an early concrete proposal of interacting particles at the ends of strings (quarks interacting with QCD flux tubes), with dynamical boundary conditions for string endpoints where the Dirichlet conditions were dynamical rather than static.
Mixed Dirichlet/Neumann boundary conditions were first considered by Warren Siegel in 1976 as a means of lowering the critical dimension of open string theory from 26 or 10 to 4 (Siegel also cites unpublished work by Halpern, and a 1974 paper by Chodos and Thorn, but a reading of the latter paper shows that it is actually concerned with linear dilation backgrounds, not Dirichlet boundary conditions).
This paper, though prescient, was little-noted in its time (a 1985 parody by Siegel, "The Super-g String", contains an almost dead-on description of braneworlds).
Dirichlet conditions for all coordinates including Euclidean time (defining what are now known as D-instantons) were introduced by Michael Green in 1977 as a means of introducing point-like structure into string theory, in an attempt to construct a string theory of the strong interaction.
String compactifications studied by Harvey and Minahan, Ishibashi and Onogi, and Pradisi and Sagnotti in 1987–1989 also employed Dirichlet boundary conditions.
This result implies that such boundary conditions must necessarily appear in regions of the moduli space of any open string theory.
D-instantons were extensively studied by Green in the early 1990s, and were shown by Polchinski in 1994 to produce the e–1⁄g nonperturbative string effects anticipated by Shenker.