Bonus Symmetry and the Operator Product Expansion of N=4 Super-Yang-Mills

Details Bonus Symmetry and the Operator Product Expansion of N=4 Super-Yang-Mills Bonus Symmetry and the Operator Product Expansion of N=4 Super-Yang-Mills

1999-05-04

arxiv.org/abs/hep-th/9905020v1

Nucl.Phys. B559 (1999) 165-183

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, 2 figures, harvmac

Scientific paper

10.1016/S0550-3213(99)00430-7

The superconformal group of N=4 super-Yang-Mills has two types of operator representations: short and long. We conjecture that operator product expansions for which at least two of the three operators are short exactly respect a bonus U(1)_Y R-symmetry, which acts as an automorphism of the superconformal group. This conjecture is for arbitrary gauge group G and gauge coupling g_{YM}. A consequence is that n\leq 4-point functions 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\leq 3 -point functions involving only short operators are not renormalized, as has also been previously conjectured and subjected to perturbative checks. It is argued that instantons are compatible with our conjecture. Some perturbative checks of the conjecture are presented and SL(2,Z) modular transformation properties are discussed.

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