Super Schrodinger algebra in AdS/CFT

TL;DR

This paper explores extended super Schrödinger algebras within the superconformal algebra psu(2,2|4), revealing new subalgebras with enhanced supersymmetry and their embeddings in AdS/CFT correspondence.

Contribution

It identifies and characterizes extended super Schrödinger subalgebras in psu(2,2|4) and related superconformal algebras, detailing their supersymmetry content and algebraic structure.

Findings

Found an extended super Schrödinger algebra with 24 supercharges in psu(2,2|4)

Identified a smaller super Schrödinger subalgebra with 8 supercharges

Discussed embeddings of these algebras in superconformal frameworks

Abstract

We discuss (extended) super Schrodinger algebras obtained as subalgebras of the superconformal algebra psu(2,2|4). The Schrodinger algebra with two spatial dimensions can be embedded into so(4,2). In the superconformal case the embedded algebra may be enhanced to the so-called super Schrodinger algebra. In fact, we find an extended super Schrodinger subalgebra of psu(2,2|4). It contains 24 supercharges (i.e., 3/4 of the original supersymmetries) and the generators of so(6), as well as the generators of the original Schrodinger algebra. In particular, the 24 supercharges come from 16 rigid supersymmetries and half of 16 superconformal ones. Moreover, this superalgebra contains a smaller super Schrodinger subalgebra, which is a supersymmetric extension of the original Schrodinger algebra and so(6) by eight supercharges (half of 16 rigid supersymmetries). It is still a subalgebra even if there are no so(6) generators. We also discuss super Schrodinger subalgebras of the superconformal algebras, osp(8|4) and osp(8^*|4).