Reference : ${\mathbb{Z}}_{2}{\times}{\mathbb{Z}}_{2}$-graded supersymmetry: 2-d sigma models
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Physics To cite this reference: http://hdl.handle.net/10993/45003
 Title : ${\mathbb{Z}}_{2}{\times}{\mathbb{Z}}_{2}$-graded supersymmetry: 2-d sigma models Language : English Author, co-author : Bruce, Andrew [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >] Publication date : Oct-2020 Journal title : Journal of Physics. A, Mathematical and Theoretical Publisher : IOP Volume : 53 Issue/season : 45 Pages : 455201 Peer reviewed : Yes (verified by ORBilu) Audience : International ISSN : 1751-8113 e-ISSN : 1751-8121 Abstract : [en] We propose a natural ${\mathbb{Z}}_{2}{\times}{\mathbb{Z}}_{2}$-graded generalisation of d = 2, $\mathcal{N}=\left(1,1\right)$ supersymmetry and construct a ${\mathbb{Z}}_{2}^{2}$-space realisation thereof. Due to the grading, the supercharges close with respect to, in the classical language, a commutator rather than an anticommutator. This is then used to build classical (linear and non-linear) sigma models that exhibit this novel supersymmetry via mimicking standard superspace methods. The fields in our models are bosons, right-handed and left-handed Majorana–Weyl spinors, and exotic bosons. The bosons commute with all the fields, the spinors belong to different sectors that cross commute rather than anticommute, while the exotic boson anticommute with the spinors. As a particular example of one of the models, we present a 'double-graded' version of supersymmetric sine-Gordon theory. Target : Researchers Permalink : http://hdl.handle.net/10993/45003 DOI : 10.1088/1751-8121/abb47f

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