Generalized action principle and extrinsic geometry for N=1 superparticle

TL;DR

This paper introduces a generalized action functional for N=1 superparticle across various dimensions, utilizing a superfield geometric approach that reveals extrinsic geometry and invariance properties, and explores interactions with Abelian gauge fields.

Contribution

It presents a novel generalized action for N=1 superparticle in multiple dimensions, incorporating extrinsic geometry and demonstrating invariance and interaction frameworks.

Findings

Derived superfield geometric equations for superparticle motion.

Proved off-shell superdiffeomorphism invariance of the generalized action.

Extended the formulation to include superparticle interactions with Abelian gauge fields.

Abstract

It is proposed the generalized action functional for N=1 superparticle in D=3,4,6 and 10 space-time dimensions. The superfield geometric approach equations describing superparticle motion in terms of extrinsic geometry of the worldline superspace are obtained on the base of the generalized action. The off-shell superdiffeomorphism invariance (in the rheonomic sense) of the superparticle generalized action is proved. It was demonstrated that the half of the fermionic and one bosonic (super)fields disappear from the generalized action in the analytical basis. Superparticle interaction with Abelian gauge theory is considered in the framework of this formulation. The geometric approach equations describing superparticle motion in Abelian background are obtained.