More super Schrodinger algebras from psu(2,2|4)

TL;DR

This paper constructs various super Schrödinger algebras with fewer supercharges from the N=4 superconformal algebra psu(2,2|4), including new algebras with N=2 and N=1 supersymmetry, and relates one to a 3D non-relativistic Chern-Simons system.

Contribution

It introduces new super Schrödinger algebras derived from psu(2,2|4) with different supersymmetry counts and symmetries, expanding the understanding of non-relativistic superconformal structures.

Findings

Constructed N=2 and N=1 superconformal algebras from psu(2,2|4)

Identified super Schrödinger subalgebras with 12 and 6 supercharges

Connected one super Schrödinger algebra to 3D non-relativistic Chern-Simons systems

Abstract

We discuss super Schrodinger algebras with less supercharges from N=4 superconformal algebra psu(2,2|4). Firstly N=2 and N=1 superconformal algebras are constructed from the psu(2,2|4) via projection operators. Then a super Schrodinger subalgebra is found from each of them. The one obtained from N=2 has 12 supercharges with su(2)^2 x u(1) and the other from N=1 has 6 supercharges with u(1)^3,. By construction, those are still subalgebras of psu(2,2|4). Another super Schrodinger algebra, which preserves 6 supercharges with a single u(1) symmetry, is also obtained from N=1 superconformal algebra su(2,2|1). In particular, it coincides with the symmetry of N=2 non-relativistic Chern-Simons matter system in three dimensions.