# F-term spontaneous breaking of 3D-SUSY an algebro-geometric treatment

## TL;DR

This paper introduces an algebraic geometric approach to analyze spontaneous F-term breaking of supersymmetry in three dimensions, providing a new perspective distinct from traditional methods used in four-dimensional SUSY.

## Contribution

It presents a novel mechanism for F-term spontaneous SUSY breaking in 3D using projective algebraic geometry, expanding the mathematical toolkit for SUSY studies.

## Key findings

- Established a result on generic exactness of SUSY in 3D
- Developed a new algebraic geometric method for SUSY analysis
- Provided a mechanism for F-term spontaneous SUSY breaking in 3D

## Abstract

We settle a result on generic exactness of SUSY in 3-D, and provide a mechanism of F-term spontaneous breaking of 3-D SUSY, with a different set of tools from those used by O'Raifeartaigh in his seminal work on 4-D SUSY. In our study, we use techniques of projective algebraic geometry so as to deal successfully with cubic hypersurfaces.