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

TL;DR

This paper develops a superfield formalism for minimal $Z_2^2$-graded supersymmetry using a new integration method on $Z_2^2$-superspace, enabling the construction of extended supersymmetric actions with novel interaction terms.

Contribution

It introduces a superfield formalism for $Z_2^2$-graded supersymmetry and constructs supersymmetric actions with general interactions, extending known theories in two dimensions.

Findings

Constructed $Z_2^2$-supersymmetric actions using superfields.

Extended the sine-Gordon model to $Z_2^2$-graded supersymmetry.

Demonstrated the formalism's ability to produce new interaction terms.

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.