A family of super Schrodinger invariant Chern-Simons matter systems

TL;DR

The paper develops non-relativistic, Schrödinger-invariant field theories by taking NR limits of a relativistic $ ext{N}=3$ Chern-Simons-matter system in 1+2 dimensions. By keeping only particle modes or by forming mixed particle/antiparticle truncations, it constructs NR theories with maximally, and variably, preserved supersymmetry, and derives their Noether Schrödinger generators. A key result is that Schrödinger symmetry persists across NR limits, while the amount of supersymmetry depends sensitively on the retained degrees of freedom, yielding NR algebras with 8 real supercharges (all-particle case) down to 2 real supercharges (PAPA case), and a systematic discussion of consistent truncations. The findings offer a framework for generating and classifying super Schrödinger invariant NR field theories and hint at applications to ABJM/AdS-CMP contexts, with implications for quantum stability and non-relativistic holography.

Abstract

We investigate non-relativistic limits of the N=3 Chern-Simons matter system in 1+2 dimensions. The relativistic theory can generate several inequivalent super Schodinger invariant theories, depending on the degrees of freedom we choose to retain in the non-relativistic limit. The maximally supersymmetric Schrodinger invariant theory is obtained by keeping all particle degrees of freedom. The other descendants, where particles and anti-particles coexist, are also Schrodinger invariant but preserve less supersymmetries. Thus, we have a family of super Schrodinger invariant field theories produced from the parent relativistic theory.