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

We investigate the low-energy effective action in N = 4 super Yang-Mills th eory 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. (C) 2000 Publ ished by Elsevier Science B.V. All rights reserved.