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arXiv · 2308.16860

$\mathbb{Z}_2^2$-graded supersymmetry via superfield on minimal $\mathbb{Z}_2^2$-superspace

N. Aizawa·Ren Ito·Toshiya Tanaka
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Abstract

A superfield formalism for the minimal $\mathbb{Z}_2^2$-graded version of supersymmetry is developed. This is done by using the recently introduced definition of integration on the minimal $\mathbb{Z}_2^2$-superspace. It is shown that one may construct $\mathbb{Z}_2^2$-supersymmetric action by the procedure similar to the standard supersymmetry. However, the Lagrangian obtained has very general interaction terms, which give rise to a $\mathbb{Z}_2^2$-graded extension of many known theories defined in two-dimensional spacetime. As an illustration, we will give a $\mathbb{Z}_2^2$-extension of the sine-Gordon model different from the one already discussed in the literature.

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N. Aizawa, Ren Ito, Toshiya Tanaka. 2023-08-31. $\mathbb{Z}_2^2$-graded supersymmetry via superfield on minimal $\mathbb{Z}_2^2$-superspace. https://doi.org/10.1088/1751-8121%2Fad811a

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