Supersymmetric Matrix model on Z-orbifold

TL;DR

This paper investigates supersymmetric properties of IIA Matrix models on various non-compact orbifolds, revealing preserved supersymmetry in these models and identifying conditions under which supersymmetry is maintained.

Contribution

It demonstrates that certain IIA Matrix models on non-compact orbifolds preserve supersymmetry, including cases with parity-like identifications, expanding understanding of supersymmetry in orbifolded spaces.

Findings

Supersymmetry is preserved in Matrix models on $C^3/Z_6$, $C^2/Z_2$, and $C^2/Z_4$ orbifolds.

The $C^3/Z_6$ orbifold model has ${ m extbf{N}=2}$ supersymmetry, same as $C^3/Z_3$.

The $C^2/Z_2$ and $C^2/Z_4$ models have half of the ${ m extbf{N}=2}$ supersymmetry.

Abstract

We find that the IIA Matrix models defined on the non-compact $C^3/Z_6$, $C^2/Z_2$ and $C^2/Z_4$ orbifolds preserve supersymmetry where the fermions are on-mass-shell Majorana-Weyl fermions. In these examples supersymmetry is preserved both in the orbifolded space and in the non-orbifolded space at the same time. The Matrix model on $C^3/Z_6$ orbifold has the same ${\cal N}=2$ supersymmetry as the case of $C^3/Z_3$ orbifold which was pointed out previously. On the other hand the Matrix models on $C^2/Z_2$ and $C^2/Z_4$ orbifold have a half of the ${\cal N}=2$ supersymmetry. We further find that the Matrix model on $C^2/Z_2$ orbifold with a parity-like identification preserves ${\cal N}=2$ supersymmetry.