Motivated by recent applications of Carroll symmetries we investigate the geometry of flat and curved (AdS) Carroll space and the symmetries of a particle moving in such a space both in the bosonic as well as in the supersymmetric case. In the bosonic case we find that the Carroll particle possesses an infinite-dimensional symmetry which only in the flat case includes dilatations. The duality between the Bargmann and Carroll algebra, relevant for the flat case, does not extend to the curved case.
In the supersymmetric case we study the dynamics of the N=1 AdS Carroll superparticle. Only in the flat limit we find that the action is invariant under an infinite-dimensional symmetry that includes a supersymmetric extension of the Lifshitz Carroll algebra with dynamical exponent z=0. We also discuss in the flat case the extension to N=2 supersymmetry and show that the flat N=2 superparticle is equivalent to the (non-moving) N=1 superparticle and that therefore it is not BPS unlike its Galilei counterpart. This is due to the fact that in this case kappa-symmetry eliminates the linearized supersymmetry.
In an appendix we discuss the N=2 curved case in three dimensions only and show that there are two N=2 theories that are physically different.
Van Swinderen Institute, University of Groningen（格罗宁根大学范斯温德伦研究所）；Universidad Católica de la Santísima Concepción（圣心天主教大学）；Grupo de Investigación en Física Teórica, GIFT, Universidad Católica de la Santísima Concepción（圣心天主教大学理论物理研究组，GIFT）；Facultad de Ingeniería, Arquitectura y Diseño, Universidad San Sebastián（圣塞巴斯蒂安大学工程、建筑与设计学院）；Division of Theoretical Physics, Rudjer Bošković Institute（鲁德·博什科维奇研究所理论物理部）
Maxwell Institute and School of Mathematics, The University of Edinburgh（爱丁堡大学数学学院）；International School for Advanced Studies (SISSA)（国际高等研究院）；Istituto Nazionale di Fisica Nucleare, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Centro de Estudios Científicos (CECs)（科学研究中心）；Facultad de Ingeniería, Universidad San Sebastián, sede Valdivia（圣塞巴斯蒂安大学工程学院（瓦尔迪维亚校区））；Erwin Schrödinger Int. Institute for Mathematics and Physics, University of Vienna（维也纳大学埃尔温·薛定谔数学与物理国际研究所）；University of Vienna, Faculty of Physics, Mathematical Physics（维也纳大学物理学院数学物理系）
Null Strings Gauged and Reloaded, I: Null Strings Have Carroll-Weyl Gauge Symmetry
School of Physics, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所物理学院）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京数学科学与应用研究院）
Krylov Complexity: Flat bands and Carroll breaking deformations
Birla Institute of Technology and Science, Pilani Campus（比拉理工学院皮拉尼校区）；Department of Physics, Indian Institute of Technology Gandhinagar（印度理工学院艾哈迈达巴德分校物理系）；Department of Physics, Birla Institute of Technology and Science Pilani, Zuarinagar, Goa（比拉理工学院扎伊纳加尔果阿校区物理系）
