(super)Schwarzian mechanics

TL;DR

This paper systematically constructs supersymmetric Schwarzians for various N-extended supersymmetries using nonlinear realizations, providing a unified approach that avoids previous restrictions.

Contribution

It introduces a new method to derive supersymmetric Schwarzians as projections of Maurer-Cartan forms without imposing restrictions, expanding the understanding of superconformal structures.

Findings

Systematic derivation of N=0,1,2,3,4 supersymmetric Schwarzians.

Construction of supersymmetric Schwarzian actions from Cartan forms.

Elimination of previous restrictions on super-Schwarzians.

Abstract

In this paper we revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that ${\cal N}=0,1,2,3,4$ supersymmetric Schwarzians can be systematically obtained as certain projections of Maurer-Cartan forms of superconformal groups after imposing simple conditions on them. We also present the supersymmetric Schwarzian actions defined as the integrals of products of Cartan forms. In contrast with the previous attempts to obtain the super-Schwarzians within nonlinear realizations technique, our set of constraints does not impose any restriction on the super-Schwarzians.