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

TL;DR

This paper conjectures a bonus U(1)_Y symmetry in N=4 super-Yang-Mills operator product expansions involving short operators, implying non-renormalization of low-point functions and compatibility with duality and instantons.

Contribution

It introduces a conjecture that a bonus U(1)_Y symmetry governs certain operator expansions in N=4 super-Yang-Mills, extending previous duality and perturbative insights.

Findings

Conjecture that short operator expansions respect U(1)_Y symmetry.

Implication that 3- and 4-point functions of short operators are not renormalized.

Discussion of instanton compatibility and modular properties.

Abstract

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.