SL(2,Z) Multiplets in N=4 SYM Theory

TL;DR

This paper explores how SL(2,Z) symmetry acts on local operators in N=4 SYM theory, revealing the multiplet structure and transformation properties, including the Konishi multiplet and its non-perturbative duals.

Contribution

It analyzes the modular transformation properties of local operators in N=4 SYM, identifying their multiplet structures under SL(2,Z) and providing insights into non-perturbative dual operators.

Findings

Operators in the Konishi multiplet form (p,q) SL(2,Z) multiplets.

The modular property of scaling dimensions determines operator transformation.

Comments on non-perturbative dual operators to the Konishi multiplet.

Abstract

We discuss the action of SL(2,Z) on local operators in D=4, N=4 SYM theory in the superconformal phase. The modular property of the operator's scaling dimension determines whether the operator transforms as a singlet, or covariantly, as part of a finite or infinite dimensional multiplet under the SL(2,Z) action. As an example, we argue that operators in the Konishi multiplet transform as part of a (p,q) PSL(2,Z) multiplet. We also comment on the non-perturbative local operators dual to the Konishi multiplet.