A simple supersymmetric extension of K field theories

TL;DR

This paper develops a simple supersymmetric extension for K field theories with kink solutions, maintaining key features like the kink solution and linear fermion equations, while revealing unique aspects such as non-equivalence of Lagrangians and absence of SUSY algebra central extension.

Contribution

It introduces a novel supersymmetric extension for K field theories with kink solutions, highlighting distinctive properties and differences from standard SUSY theories.

Findings

Fermion equations are linear and solved by the first derivative of the kink.

The bosonic part of the SUSY Lagrangian differs from the original K field Lagrangian.

No central extension appears in the SUSY algebra despite kink solutions.

Abstract

We continue the investigation of supersymmetric extensions of field theories with a non-standard kinetic term (K field theories) resumed recently. Concretely, for K field theories which allow for kink or compacton solutions in 1+1 dimensions, i.e., for domain walls in a higher-dimensional context, we find a simple supersymmetric extension such that the boson field still has the kink solution, and the field equation for the fermion in the kink background is linear and is solved by the first spatial derivative of the kink, as is the case in the corresponding standard supersymmetric theories. This supersymmetric extension, nevertheless, is peculiar in several aspects. The bosonic part of the supersymmetric Lagrangian is not equal to the original bosonic K field Lagrangian, but the bosonic field equations coincide. Further, the field equation for the bosonic field is produced by the variation of the auxiliary field and vice versa. This observation may be of some independent interest. Finally, the presence of kink solutions does not lead to a central extension in the SUSY algebra, in contrast to the standard case.