Article (Scientific journals)
${\mathbb{Z}}_{2}{\times}{\mathbb{Z}}_{2}$-graded supersymmetry: 2-d sigma models
BRUCE, Andrew
2020In Journal of Physics. A, Mathematical and Theoretical, 53 (45), p. 455201
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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.
Disciplines :
Physics
Author, co-author :
BRUCE, Andrew ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
External co-authors :
no
Language :
English
Title :
${\mathbb{Z}}_{2}{\times}{\mathbb{Z}}_{2}$-graded supersymmetry: 2-d sigma models
Publication date :
October 2020
Journal title :
Journal of Physics. A, Mathematical and Theoretical
ISSN :
1751-8113
eISSN :
1751-8121
Publisher :
IOP
Volume :
53
Issue :
45
Pages :
455201
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 14 December 2020

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