The affine ambitwistor space as the moduli space of SUYM in $Ad{S}_5\otimes S^5$

By extending the dressing symmetric action of IIB string in $Ad{S}_5\times S^5$ to the $D_3$ brane, we find a gauged WZW action of Higgs Yang-Mills field including the 2-cocycle of axially anomaly. The left and right twistor structure of left and right $\alpha$-planes glue into an ambitwistor. The symmetry group of Nahm equations is central extended to an affine group, thus we explain why the spectral curve is given by affine Toda.