Schwarzian derivative treatment of the quantum second-order supersymmetry anomaly, and coupling-constant metamorphosis

TL;DR

This paper explores how the Schwarzian derivative can be used to address quantum anomalies in supersymmetric systems with second-order supercharges, and introduces a method to relate systems with different supersymmetry orders through coupling-constant metamorphosis.

Contribution

It establishes a link between the Schwarzian derivative and quantum anomalies in supersymmetry, providing a new quantization scheme to eliminate anomalies and connecting systems with different supersymmetry orders.

Findings

Identified the role of the Schwarzian derivative in quantum anomalies.

Developed a quantization prescription for anomaly-free supersymmetric systems.

Demonstrated the coupling-constant metamorphosis between different supersymmetry orders.

Abstract

A canonical quantization scheme applied to a classical supersymmetric system with quadratic in momentum supercharges gives rise to a quantum anomaly problem described by a specific term to be quadratic in Planck constant. We reveal a close relationship between the anomaly and the Schwarzian derivative, and specify a quantization prescription which generates the anomaly-free supersymmetric quantum system with second order supercharges. We also discuss the phenomenon of a coupling-constant metarmorphosis that associates quantum systems with first-order supersymmetry to the systems with the second-order supercharges.