Super Schrodinger algebra in AdS/CFT

TL;DR

The paper identifies extended (and reduced) super Schrödinger subalgebras embedded in psu(2,2|4) and in the related osp(8|4) and osp(8^*|4) superconformal algebras. It constructs these algebras by decomposing the parent superalgebras into conformal and R-symmetry sectors and using chirality/projectors to isolate fermionic generators, yielding an extended algebra with 24 supercharges and an so(6) (su(4)) R-symmetry. A smaller eight-supercharge subalgebra is also found, which can exist without the so(6) sector. The work lays groundwork for non-relativistic holography by suggesting coset constructions and potential CFT actions with maximal super Schrödinger symmetry, and it points to broader classification and generalization to other superconformal algebras.

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).