{"arxiv_id":"hep-th/0508079","title":"On Schr\\\"odinger superalgebras","abstract":"We construct, using the supersymplectic framework of Berezin, Kostant and others, two types of supersymmetric extensions of the Schr\\\"odinger algebra (itself a conformal extension of the Galilei algebra). An `$I$-type' extension exists in any space dimension, and for any pair of integers $N_+$ and $N_-$. It yields an $N=N_++N_-$ superalgebra, which generalizes the N=1 supersymmetry Gauntlett et al. found for a free spin-$\\half$ particle, as well as the N=2 supersymmetry of the fermionic oscillator found by Beckers et al. In two space dimensions, new, `exotic' or `$IJ$-type' extensions arise for each pair of integers $\\nu_+$ and $\\nu_-$, yielding an $N=2(\\nu_++\\nu_-)$ superalgebra of the type discovered recently by Leblanc et al. in non relativistic Chern-Simons theory. For the magnetic monopole the symmetry reduces to $\\o(3)\\times\\osp(1/1)$, and for the magnetic vortex it reduces to $\\o(2)\\times\\osp(1/2)$.","primary_cat":"hep-th","cross_cats":[],"submitted_at":"2005-08-11T08:26:49+00:00","latest_version":1,"source":"arxiv","source_label":"arXiv","source_url":null,"has_pdf":true,"has_source":false,"verdict":"ACCEPT","confidence":"MODERATE","one_line_summary":"Two families of super-Schrödinger algebras are constructed: an I-type existing in any dimension for any (N+, N-), and a two-dimensional exotic IJ-type that reproduces the Leblanc-Lozano-Min Chern-Simons superalgebra as a special case.","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","upvotes":0,"downvotes":0,"pith_score":0.0,"inbound_count":13,"_links":{"html":"https://pith.science/paper/hep-th/0508079","verdict":"/api/v1/verdicts/hep-th/0508079"}}