Reconstruction of N=1 supersymmetry from topological symmetry

TL;DR

This paper demonstrates how topological symmetries on Calabi-Yau manifolds can be used to reconstruct various N=1 supersymmetric Yang-Mills theories in different dimensions, revealing a geometric origin of supersymmetry.

Contribution

It shows that topological symmetries on Calabi-Yau manifolds fully determine N=1 supersymmetric Yang-Mills actions across multiple dimensions, unifying their geometric origin.

Findings

Reconstruction of N=1, D=4 Wess-Zumino and superYang-Mills theories from topological symmetry.

Introduction of superpotential and Fayet-Iliopoulos mechanism within this framework.

Extension to N=1, D=6 Yang-Mills theory on CY_3 manifolds.

Abstract

The scalar and vector topological Yang-Mills symmetries on Calabi-Yau manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1 supersymmetry, which fully determine the supersymmetric actions up to twist. For a CY_2 manifold, both N=1,D=4 Wess and Zumino and superYang-Mills theory can be reconstructed in this way. A superpotential can be introduced for the matter sector, as well as the Fayet-Iliopoulos mechanism. For a CY_3 manifold, the N=1, D=6 Yang-Mills theory is also obtained, in a twisted form. Putting these results together with those already known for the D=4,8 N=2 cases, we conclude that all Yang--Mills supersymmetries with 4, 8 and 16 generators are determined from topological symmetry on special manifolds.