  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.
