N=4 super Yang–Mills low-energy effective action at three and four loops

We investigate the low-energy effective action in N=4 super Yang–Mills theory with gauge group SU(n) spontaneously broken down to its maximal torus. Using harmonic superspace technique we prove an absence of any three- and four-loop corrections to non-holomorphic effective potential depending on N=2 superfield strengths. A mechanism responsible for vanishing arbitrary loop corrections to low-energy effective action is discussed.