Analysis of the superconformal cohomology structure of N=4 super Yang-Mills

The nilpotent symmetry operator for the full superconformal symmetry of N=4 super Yang-Mills is constructed using the method of Batalin and Vilkovisky (1977). Spectral sequences are then used to prove that the cohomology of this operator is trivial, and so the theory has no possible anomalies. This shows that all symmetries are preserved after quantization, and so there is no conformal anomaly and the theory is thus finite to all orders.