Higher-Derivative Supersymmetry and the Witten Index

TL;DR

This paper introduces a higher-derivative extension of supersymmetric quantum mechanics where supercharges involve higher-order differential operators, leading to a polynomial relation with the Hamiltonian and altering the role of the Witten index.

Contribution

It proposes a novel higher-derivative supersymmetric quantum mechanics framework with supercharges of order n, expanding the algebraic structure beyond standard models.

Findings

Supercharges involve differential operators of order n.

Anticommutator yields a polynomial of the Hamiltonian.

Witten index does not indicate supersymmetry breaking in these models.

Abstract

Higher-derivative generalization of the supersymmetric quantum mechanics is proposed. It is formally based on the standard superalgebra but supercharges involve differential operators of the order $n$. As a result, their anticommutator entails polynomial of a Hamiltonian. The Witten index does not characterize spontaneous supersymmetry breaking in such models.