Superconformal Mechanics and the Super Virasoro Algebra

TL;DR

This paper explores the structure of superconformal mechanics in one dimension, demonstrating how super Virasoro algebra can be constructed from superconformal generators under certain conditions, with a focus on quantization and algebraic relations.

Contribution

It provides a general method to derive the super Virasoro algebra from superconformal mechanics, applicable when the Hamiltonian and special conformal generator are invertible and the Casimir vanishes.

Findings

Superconformal generators form half of the super Virasoro algebra when Hamiltonian is invertible.

Full super Virasoro algebra is obtained if the special conformal generator is also invertible.

A quantization procedure for the generators is established, independent of specific mechanics details.

Abstract

We consider N=1,2 superconformal mechanics in 0+1 dimensions and show that if the Hamiltonian is invertible the superconformal generators can be used to construct half of the super Virasoro algebra. The full algebra can be derived if the special conformal generator is also invertible. The generators are quantized and a general prescription is given for the construction of the N=1 algebra independently of the specific details of the superconformal mechanics provided that in addition its quadratic Casimir operator vanishes.