Bonus symmetry and the operator product expansion of N=4 super-Yang-Mills

The superconformal group of N = 4 super-Yang-Mills has two types of operato r representations: short and long. We conjecture that operator product expa nsions for which at least two of the three operators are short exactly resp ect a bonus U(1)(Y) R-symmetry, which acts as an automorphism of the superc onformal group. This conjecture is for arbitrary gauge group G and gauge co upling g(YM). A consequence is that n less than or equal to 4-point functio ns involving only short operators exactly respect the U(1)(Y) symmetry, as has been previously conjectured based on AdS duality. This, in turn, would imply that all n less than or equal to 3-point functions involving only sho rt operators are not renormalized, as has also been previously conjectured and subjected to perturbative checks. It is argued that instantons are comp atible with our conjecture. Some perturbative checks of the conjecture are presented and SL(2, Z) modular transformation properties are discussed. (C) 1999 Elsevier Science B.V. All rights reserved.