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arXiv · 1905.06548

$\cal N$-Extension of duble-graded supersymmetric and superconformal quantum mechanics

N. Aizawa·K. Amakawa·S. Doi
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Abstract

In the recent paper, Bruce and Duplij introduced a double-graded version of supersymmetric quantum mechanics (SQM). It is an extension of Lie superalgebraic nature of ${\cal N}=1$ SQM to a $\mathbb{Z}_2^2$-graded superalgebra. In this work, we propose an extension of Bruce-Duplij model to higher values of $\cal N.$ Furthermore, it is shown that our construction of double-graded SQM is a special case of the method which converts a given Lie superalgebra to a $\mathbb{Z}_2^2$-graded superalgebra. By employing this method one may convert a model of superconformal mechanics to its double-graded version. The simplest example of ${\cal N}=1$ double-graded superconformal mechanics is studied in some detail.

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N. Aizawa, K. Amakawa, S. Doi. 2019-05-16. $\cal N$-Extension of duble-graded supersymmetric and superconformal quantum mechanics. https://doi.org/10.1088/1751-8121%2Fab661c

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