About the Non Relativistic Structure of the AdS/CFT Superalgebras

TL;DR

This paper extends the relationship between conformal and Schr"odinger algebras to supersymmetric cases, identifying superalgebra structures that generalize known non-supersymmetric features.

Contribution

It determines the supersymmetric counterparts of super conformal algebras and shows their basis decomposes into two super Schr"odinger algebras, generalizing previous non-supersymmetric results.

Findings

Superalgebra structures are identified as extensions of conformal algebras.

All superalgebras decompose into two super Schr"odinger algebras with different super Heisenberg parts.

The decomposition pattern observed in non-supersymmetric cases also holds in supersymmetric cases.

Abstract

The property of the conformal algebra to contain the Schr\"odinger algebra in one less space dimension is extended to the supersymmetric case. More precisely, we determine the counterpart of any field theory admissible super conformal algebra. Even if each type of superalgebra provides a different solution, its basis decomposition into two copies of the super Schr\"odinger algebra, differing only by their super Heisenberg part, remains valid in all the cases, so generalizing a feature already observed in the non supersymmetric conformal case.