D-Brane

String Theory
All Roads Lead to String Theory (Polchinski)
Prior to the First Superstring Revolution
Early History	S-Matrix Theory Regge Trajectory
Bosonic String Theory	Worldsheet String Bosonic String Theory String Perturbation Theory Tachyon Condensation
Supersymmetric Revolution	Supersymmetry RNS Formalism GS Formalism BPS
Superstring Revolutions
First Superstring Revolution	GSO Projection Type II String Theory Type IIB String Theory Type IIA String Theory Type I String Theory Type H String Theory Type HO String Theory Type HE String Theory
Second Superstring Revolution	T-Duality D-Brane S-Duality Horava-Witten String Theory M-Theory Holographic Principle N=4 Super-Yang-Mills Theory AdS CFT BFSS Matrix Theory Matrix String Theory (2,0) Theory Twistor String Theory F-Theory String Field Theory Pure Spinor Formalism
After the Revolutions
Phenomenology	String Theory Landscape Minimal Supersymmetric Standard Model String Phenomenology

A D-Brane is a strongly coupled $p$-dimensional object that appears in String Theory, whose existence is required by T-Duality and is motivated by Ramond-Ramond Charges.

From Ramond-Ramond Charges

This article or section 's content is very similar or exactly the same as that at a Physics Stack Exchange tag wiki or post. This is because the contributor of this article had initially contributed it to Physics Stack Exchange.

The worldsheet of a string can couple to a Neveu-Schwarz B-field: $q\int _{}^{}{{h^{ab}}{\frac {\partial {X^{\mu }}}{\partial {\xi ^{a}}}}{\frac {\partial {X^{\nu }}}{\partial {\xi ^{b}}}}B_{\mu \nu }{\sqrt {-\det {h_{ab}}}}{{\text{d}}^{2}}\xi }$ Now, the $q$ is the EM-charge.

The worldsheet of a string can couple to graviton field (spacetime metric):

$m\int _{}^{}{{h^{ab}}{\frac {\partial {X^{\mu }}}{\partial {\xi ^{a}}}}{\frac {\partial {X^{\nu }}}{\partial {\xi ^{b}}}}g_{\mu \nu }{\sqrt {-\det {h_{ab}}}}{{\text{d}}^{2}}\xi }$

You can change the "$m$" to any way you like, in terms of the tension/Regge Slope parameter/string length etc.

For a dilaton field,

${q}\ell _{P}^{2}\int _{}^{}{\Phi R{\sqrt {-\det {h_{\alpha \beta }}}}{\text{ }}{{\text{d}}^{2}}\xi }$ Forget the conformal invariance for the time being. But what about Ramond-Ramond potentials? All is fine with the Ramond-Ramond Fields, but the Ramond-Ramond Potentials $C_{k}$ are associated with the Ramond-Ramond field $A_{k+1}$ and it is intuitive (and quite clear) that they can't couple similarly to the worldsheet. But it can for a worldhhypervolume, as long as the world-hypervolume is not 2-dimensional. It would then be given by:

${q_{\text{RR}}}\int _{}^{}{C_{{\mu _{1}}...{\mu _{p}}}^{p+1}{\frac {\partial {x^{\mu _{1}}}}{\partial {\xi ^{a_{1}}}}}...{\frac {\partial {x^{\mu _{p}}}}{\partial {\xi ^{a_{p}}}}}{h^{{a_{0}}...{a_{p}}}}{\sqrt {-\det {h^{{a_{0}}...{a_{p}}}}}}{{\text{d}}^{p+1}}\xi }$

Note the similarity to the other couplings. Of course, this does not really neccessitate the existence of D-Branes though.

From T-Duality

Considering T-Duality on open strings immediately realises that open strings with Newmann boundary conditions ("Free" strings) are mapped to those with Dirchilet boundary conditions ("Bound" strings). These "bound" strings must be attached to D-branes. Therefore, strings with Newmann boundary conditions in a String Theory would have Dirchilet boundary conditions in the T-dual theory.

Therefore, this requires the existence of D-Branes.