Weak supersymmetry and superconformal indices

TL;DR

This paper explores weak supersymmetry in quantum mechanics, relating it to higher-order models, and computes superconformal indices showing their equivalence to Witten indices in second-order supersymmetry.

Contribution

It introduces matrix form models of weak supersymmetry and calculates their superconformal indices, establishing their relation to existing supersymmetric indices.

Findings

Superconformal indices are computed for weak supersymmetry models.

Indices are shown to be equivalent to Witten indices in second-order supersymmetric quantum mechanics.

Models relate to parasupersymmetric and higher-derivative deformations.

Abstract

One-dimensional quantum mechanical models obeying Smilga's weak supersymmetry are described in the matrix form. They are related to the parasupersymmetric and higher-order derivative deformations of the standard supersymmetric models discussed earlier. Their superconformal indices are computed and shown to be equivalent to the Witten indices for the second order supersymmetric quantum mechanics.