An unconventional supergravity

TL;DR

This paper introduces a new supergravity framework by defining curvature tensors on a supergrassmannian related to Minkowski space, providing insights into supersymmetric theories and counterexamples to established theorems.

Contribution

It develops the analogues of the Riemann curvature tensor for a specific supergrassmannian, expanding the mathematical tools for supergravity and supersymmetry research.

Findings

Defined curvature tensors for the supergrassmannian

Connected the supergrassmannian to Minkowski space

Provided a counterexample to Coleman-Mandula's theorem

Abstract

We introduce and completely describe the analogues of the Riemann curvature tensor for the curved supergrassmannian of the passing through the origin (0|2)-dimensional subsupermanifolds in the (0|4)-dimensional supermanifold with the preserved volume form. The underlying manifold of this supergrassmannian is the conventional Penrose's complexified and compactified version of the Minkowski space, i.e., the Grassmannian of 2-dimensional subspaces in the 4-dimensional space. The result provides with yet another counterexample to Coleman-Mandula's theorem.