Superconformal Structures and the Superparticle on the Complex Projective Line

TL;DR

This paper introduces superconformal structures on supermanifolds to analyze the superparticle sigma-model, focusing on the relationship between Lagrangians and the integration of variations, with illustrations on the complex projective line.

Contribution

It develops a new framework for superconformal structures and explores their application to the superparticle sigma-model on the complex projective line.

Findings

Established a link between superparticle and component Lagrangians.

Addressed the integration of infinitesimal variations into global variations.

Provided explicit examples on the complex projective line.

Abstract

In this paper the notion of a superconformal structure on a supermanifold is introduced in an effort to study the superparticle sigma-model. There are, in particular, two main aspects of the sigma-model which are investigated. The first is on the relationship between the superparticle Lagrangian and the component Lagrangian; and the second is on the problem of integrating infinitesimal variations to globally-defined variations of the component Lagrangian, which leads naturally to a notion of consistency. Throughout this paper illustrations are provided on the complex projective line.