SUSY structures on deformed supermanifolds

TL;DR

This paper develops a geometric framework for deformed supermanifolds, revealing how supersymmetry algebra emerges in the semiclassical limit and detailing high energy corrections for mass-preserving cases.

Contribution

It introduces a new geometric structure on deformed supermanifolds that captures supersymmetry algebra and its high energy corrections.

Findings

In the classical limit, odd and even transformations decouple.

In the semiclassical limit, the structure yields a supersymmetry algebra representation.

High energy corrections are characterized for mass-preserving structures.

Abstract

We construct a geometric structure on deformed supermanifolds as a certain subalgebra of the vector fields. In the classical limit we obtain a decoupling of the infinitesimal odd and even transformations, whereas in the semiclassical limit the result is a representation of the supersymmetry algebra. In the case of mass preserving structure we describe all high energy corrections to this algebra.