Superconformal transformations of the N = 4 supersymmetric

The N = 4 supersymmetric Yang-Mills theory (SSYM) has many interesting properties, one of them being its finiteness to all orders in perturbation (Mandelstam 1983; Howe et a11983; Brink et al 1983; Salam et a11983). One of the ways to prove finiteness (Sohnius and West 1981), relies on the fact that the N = 4 superconformal (SC) algebra does not involve the chiral-R charge. In this paper we obtain the SC transformation laws for the N = 4 SSYM supermultiplet and explicitly verify that the representation of the SC algebra does not involve R charge as expected. We give a simple way of obtaining the SC transformation laws and explicitly verify the closure of the algebra. The N = 4 SC algebra is well known (Sohnius 1985). In addition to the usual fifteen generators of the conformal group, the N = 4 SC algebra in 3 + 1 dimensions consists of eight four-component Majorana fermionic charges corresponding to the SUSY charges Q~i and SC charges SMi, i = 1 4, where M implies the Majorana fermions. These fermionic charges can be expressed in terms of eight two-component Weyl fermionic charges Q~ and Si~ and their hermitian conjugates (~,~ and ~ (~ and ~/are Weyl fermion indices) as,