D2brane

D2-brane is a two-dimensional spatial D-brane in Type II string theory. It is a dynamical object on which open strings can end and which carries Ramond-Ramond charge under the C3 form. The worldvolume of a D2-brane is three-dimensional, consisting of two spatial directions and time.

Worldvolume theory: For N coincident D2-branes the low-energy dynamics is a 2+1 dimensional U(N) supersymmetric gauge theory with seven scalar fields corresponding to fluctuations in the transverse directions and fermions completing the multiplet. A single D2-brane gives a U(1) gauge theory with seven scalars; multiple branes yield non-abelian gauge symmetry. The gauge fields and scalars describe fluctuations along and transverse to the brane.

Action and couplings: The dynamics are governed by the Dirac-Born-Infeld action with a Wess-Zumino term. For a stack of N D2-branes the worldvolume theory includes a U(N) gauge field and seven transverse scalars, with couplings to the background Ramond-Ramond fields through the Wess-Zumino term. The tension is T2 = 1/((2π)^2 α'^{3/2} g_s), and the full action contains the pullback of the ambient metric and background fields, as well as the Born-Infeld and Chern-Simons couplings.

Geometric and duality roles: D2-branes can wrap supersymmetric cycles in compactifications, yielding lower-dimensional gauge theories on their worldvolume. They lift to M2-branes in M-theory at strong coupling, providing a unifying perspective. In Hanany–Witten type setups with NS5-branes, D2-branes realize three-dimensional gauge theories with matter content. Euclidean D2-branes (D2-instantons) can generate non-perturbative effects in the effective theory.

Stability and supersymmetry: D2-branes can preserve a portion of background supersymmetry depending on their orientation and the ambient geometry, leading to BPS configurations calibrated by the ambient structure.