Nonlinear realizations of the (super)diffeomorphism groups, geometrical objects and integral invariants in the superspace

TL;DR

This paper demonstrates that vielbeins and connections in (super)spaces can be described via nonlinear realizations of infinite-dimensional diffeomorphism groups, and extends the construction of integral invariants to superspaces.

Contribution

It introduces a unified approach to describe geometric objects in (super)spaces using nonlinear realizations and generalizes invariant integral construction to superspaces.

Findings

Vielbeins and connections are naturally described by nonlinear realizations.

The method for constructing integral invariants is extended to superspaces.

Provides a geometric framework for superspace invariants.

Abstract

It is shown that vielbeins and connections of any (super)space are naturally described in terms of nonlinear realizations of infinite - dimensional diffeomorphism groups of the corresponding (super)space. The method of construction of integral invariants from the invariant Cartan's differential $\Omega$ - forms is generalized to the case of superspace.