Dpbranes

Dp-branes (p-dimensional D-branes) are p-dimensional extended objects in string theory on which open strings can end. In type II string theories they appear as non-perturbative, solitonic configurations that carry Ramond-Ramond (RR) charge and provide loci where gauge fields propagate on their worldvolumes. They are dynamical objects with tension and charge, and their presence modifies the background through their RR couplings.

In type II theories the allowed values of p are restricted: in Type IIA, p is even (p = 0, 2, 4, 6, 8); in Type IIB, p is odd (p = 1, 3, 5, 7, 9). Each Dp-brane carries a tension T_p and couples to a (p+1)-form RR potential, with the RR charge μ_p matching the tension in the appropriate units. The effective worldvolume action of a Dp-brane includes a Dirac-Born-Infeld (DBI) term and a Chern-Simons (CS) coupling to RR fields, describing both the brane’s dynamics and its interactions with background fields.

The low-energy effective theory on a single Dp-brane is a U(1) gauge theory in p+1 dimensions, with scalar fields corresponding to transverse fluctuations. For N coincident Dp-branes, the worldvolume theory becomes U(N) supersymmetric gauge theory with adjoint scalars, arising from open strings stretching between branes. The brane system preserves a portion of the ambient supersymmetry, often forming a BPS configuration in flat space.

Dp-branes are central to many string-theory constructions and dualities. They underpin AdS/CFT realizations (for example, D3-branes yield N=4 super Yang-Mills in four dimensions and AdS5×S5), enable gauge theory engineering via brane configurations, and facilitate the study of gauge dynamics, compactifications, and brane-world scenarios.