Dbranes

D-branes, short for Dirichlet-branes, are dynamical extended objects in string theory on which open strings can end with Dirichlet boundary conditions in the directions transverse to the brane. A Dp-brane has p spatial dimensions, so its worldvolume is p+1 dimensional. They carry Ramond-Ramond charges and have a tension that scales inversely with the string coupling, making them non-perturbative objects from the viewpoint of perturbative strings.

The endpoints of open strings are confined to D-branes, giving rise to gauge fields and matter that live on the brane worldvolume. The low-energy effective action on a single Dp-brane is described by the Dirac-Born-Infeld action, which includes a U(1) gauge field and scalar fields corresponding to the brane’s transverse fluctuations. When multiple Dp-branes coincide, open strings stretching between different branes yield non-Abelian gauge fields, enhancing the symmetry to U(N) on the brane stack.

D-branes come in various dimensionalities depending on the string theory: in Type IIA theories, even p values (0, 2, 4, 6, 8) occur; in Type IIB theories, odd p values (1, 3, 5, 7, 9) occur. They couple to RR (p+1)-form potentials via a Chern-Simons term on their worldvolume, and they can form bound states with lower-dimensional branes through various charge and flux configurations.

D-branes are central to non-perturbative string dynamics and dualities. Stacks of D3-branes realize four-dimensional N=4 super Yang-Mills theory, and their near-horizon geometry leads to AdS5 × S5 and the AdS/CFT correspondence. They also participate in brane creation phenomena (Hanany-Witten effects) and transform under T- and S-duality into other branes and NS-branes. Applications span gauge/gravity duality, brane-world scenarios, and string phenomenology.