A New Superconformal Mechanics

TL;DR

This paper introduces a novel supersymmetric extension of conformal mechanics, utilizing Grassmann variables and geometric interpretations, providing new insights into the algebraic structure and solutions of the system.

Contribution

It presents a new supersymmetric extension of conformal mechanics with geometric interpretation and explicit superalgebra construction, extending the original Hamiltonian and generators.

Findings

Supersymmetric Hamiltonian is the Lie-derivative of the conformal flow.

Exact solutions derived using superfield constraints.

Superalgebra closure with integer representation on odd parts.

Abstract

In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our supersymmetric Hamiltonian itself turns out to have a clear geometrical meaning being the Lie-derivative of the Hamiltonian flow of conformal mechanics. Using superfields we derive a constraint which gives the exact solution of the supersymmetric system in a way analogous to the constraint in configuration space which solved the original non-supersymmetric model. Besides the supersymmetric extension of the original Hamiltonian, we also provide the extension of the other conformal generators present in the original system. These extensions have also a supersymmetric character being the square of some Grassmannian charge. We build the whole superalgebra of these charges and analyze their closure. The representation of the even part of this superalgebra on the odd part turns out to be integer and not spinorial in character.