A Note on Supersymmetries in AdS_5/CFT_4

TL;DR

This paper clarifies the relationship between supersymmetries in N=4 super Yang-Mills theory and those in the AdS_5 x S^5 background by deriving the superconformal algebra and mapping the generators explicitly.

Contribution

It provides a transparent derivation of the N=4 superconformal algebra from field symmetries using a Majorana-Weyl spinor in D=10, and explicitly maps supersymmetries between the gauge theory and AdS background.

Findings

Explicit map between N=4 SYM supersymmetries and AdS_5 x S^5 supersymmetries

Derivation of superconformal algebra from field transformations

Use of Majorana-Weyl spinor simplifies the relation

Abstract

The N=4 superconformal algebra is derived from the symmetry transformations of fields in the N=4 SYM action in D=4. We use a Majorana-Weyl spinor in D=10 instead of four Weyl spinors in D=4. This makes it transparent to relate generators of the N=4 superconformal algebra to those of the super-AdS_5XS^5 algebra. Especially, we obtain the concrete map from the supersymmetries Q and conformal supersymmetries S in N=4 SYM to the supersymmetries (Q_1, Q_2) in the AdS_5XS^5 background.