The affine ambitwistor space as the moduli space of SUYM in $AdS_5\otimes S^5$

By extending the dressing symmetric action of IIB string in $AdS_5\times S^5$ 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.
Comment: v2: strongly revised version (especially in important section 5), notation unified, typos corrected, referrences added