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

TL;DR

This work develops a framework in which vielbeins and connections of both bosonic and superspace arise from nonlinear realizations of the (super)diffeomorphism group, with Cartan's invariant one-form $\\Omega$ as the central building block. In the bosonic sector, the approach yields a torsionless connection and reproduces the Einstein–Hilbert action after eliminating auxiliary coset fields, linking diffeomorphisms to gravity via a coset construction. In superspace, the authors extend the formalism to graded coordinates, derive the supervielbein and its Berezinian, and show that certain torsion components vanish automatically; they also generalize the Bernstein–Leites method to construct diffeomorphism-invariant integrals, introducing auxiliary variables and ghosts to form invariants proportional to the superdeterminant Ber, while leaving open the existence of a corresponding supergravity action within this scheme. The work provides a geometric interpretation of higher-order coset parameters and a toolkit for building invariant objects in superspace, highlighting open questions about explicit actions and the role of gamma matrices in breaking tangent-space gauge groups.

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 $Ω$ - forms is generalized to the case of superspace.