D3branes

D3-branes are a class of Dirichlet branes in Type IIB string theory. They are extended along three spatial dimensions, so their worldvolume is four-dimensional (including time), and they are localized at points in the six transverse dimensions. Open strings ending on D3-branes satisfy Dirichlet boundary conditions in the transverse directions.

A stack of N coincident D3-branes hosts a four-dimensional, maximally supersymmetric gauge theory on its worldvolume: N=4 SU(N) super Yang-Mills theory. The massless modes of the open strings furnish gauge fields, six scalar fields, and fermions in the adjoint representation. The gauge coupling is g_YM^2 = 4π g_s.

D3-branes are charged under the Ramond–Ramond 4-form C4 and couple to it via the Wess–Zumino term. They have tension T3 = 1/((2π)^3 α'^2 g_s) and are BPS, preserving half of the background supersymmetry when static.

With N branes, their backreaction produces a throat that, in the near-horizon limit, becomes AdS5 × S5 with radius L given by L^4 = 4π g_s N α'^2. The five-form flux through S5 is quantized in units of N.

This setup underpins the AdS/CFT correspondence, relating Type IIB string theory on AdS5 × S5 with N units of flux to 4d N=4 SU(N) super Yang–Mills theory. D3-branes thus provide a concrete link between gauge theories and gravity, and their separations correspond to moving onto the Coulomb branch, breaking SU(N) to a product of U(1)s.