More on Two-Dimensional $O(N)$ Models with $\mathcal{N} = (0,1)$ Supersymmetry

TL;DR

This paper investigates two-dimensional $O(N)$ models with $ abla=(0,1)$ supersymmetry, revealing conditions under which supersymmetry remains unbroken despite a vanishing Witten index, due to a $Z_n$ symmetry.

Contribution

It introduces a new class of connected $O(N)$ models with $ abla=(0,1)$ supersymmetry and analyzes their vacuum structure and supersymmetry preservation conditions.

Findings

SUSY remains unbroken for even $n$ due to $Z_n$ symmetry.

Effective potential computed in large $N$ limit shows SUSY preservation.

Modified Witten index explains SUSY stability despite vanishing traditional index.

Abstract

We study the behavior of two dimensional supersymmetric connections of $n$ copies of $O(N)$ models with an $\mathcal{N} = (0,1)$ heterotic deformation generated by a right moving fermion. We develop the model in analogy with the connected $\mathcal{N}=(0,2)$ $CP(N-1)$ models for the case of a single connecting fermionic superfield. We calculate the effective potential in the large $N$ limit and determine the vacuum field configurations. Similarily to other SUSY connected models we find that SUSY is unbroken under certain conditions despite the vanishing of the Witten index. Specifically, this preservation of SUSY occurs when we have an even number $n$ of $O(N)$ families. As in previous cases we show that this result follows from a $Z_n$ symmetry under a particular exchange of the $O(N)$ families. This leads to a definition of a modified Witten index, which gaurantees the preservation of SUSY in this case.