Finiteness preserving mass terms in N=4 super Yang-Mills theory

Abstract

It is shown using light cone gauge techniques that N=4 super Yang-Mills theory is ultraviolet finite in the presence of a wide range of explicit symmetry breaking mass terms for (a) scalars and fermions (b) scalars alone. These mass terms satisfy sum rules that are part of the more general sum rule: ∑ s=0, 1 2 ,1 (−1) 2s+1(2s+1)m s 2=0 , in which the mass of vector bosons is set to zero for reasons of gauge invariance. The resulting lagrangains offer the exciting possibility of releasing explicit hierachical descent of N=4 super Yang-Mills through N=2 and N=1 supersymmetries. Tree level spontaneous symmetry breaking from the resulting scalar potentials are briefly discussed.