  Large $N_c$ and holographic arguments, as well as Monte Carlo results,
suggest that the topological structure of the QCD vacuum is dominated by
codimension-one membranes which appear as thin dipole layers of topological
charge. Such membranes arise naturally as $D6$ branes in the holographic
formulation of QCD based on IIA string theory. The polarizability of these
membranes leads to a vacuum energy $\propto \theta^2$, providing the origin of
nonzero topological susceptibility. Here we show that the axial U(1) anomaly
can be formulated as anomaly inflow on the brane surfaces. A 4D gauge
transformation at the brane surface separates into a 3D gauge transformation of
components within the brane and the transformation of the transverse component.
The in-brane gauge transformation induces currents of an effective Chern-Simons
theory on the brane surface, while the transformation of the transverse
component describes the transverse motion of the brane and is related to the
Ramond-Ramond closed string field in the holographic formulation of QCD. The
relation between the surface currents and the transverse motion of the brane is
dictated by the descent equations of Yang-Mills theory.
