Highly effective action from large $N$ gauge fields

Recently Schwarz put forward a conjecture that the world-volume action of a probe D3-brane in an ${\mathrm{AdS}}_5\times {\mathbb{S}}^5$ background of type IIB superstring theory can be reinterpreted as the highly effective action (HEA) of four-dimensional $\mathcal{N}=4$ superconformal field theory on the Coulomb branch. We argue that the HEA can be derived from the noncommutative (NC) field theory representation of the AdS/CFT correspondence and the Seiberg-Witten (SW) map defining a spacetime field redefinition between ordinary and NC gauge fields. It is based only on the well-known facts that the master fields of large $N$ matrices are higher-dimensional NC $U(1)$ gauge fields and the SW map is a local coordinate transformation eliminating $U(1)$ gauge fields known as the Darboux theorem in symplectic geometry.