Symmetries, higher order symmetries and supersymmetries

TL;DR

This paper explores a geometric Gauge-Natural framework for gauge theories, demonstrating its application to the Wess-Zumino model and discussing challenges in embedding minimal supergravity due to on-shell closure issues.

Contribution

It introduces a Gauge-Natural geometric formulation for gauge theories and applies it to the Wess-Zumino model, highlighting the need for further work on supergravity integration.

Findings

Wess-Zumino model fits within the Gauge-Natural formalism

Embedding minimal supergravity requires additional investigation

Closure of SUSY algebra occurs on-shell

Abstract

We discuss a geometrical formulation for gauge field theories, called Gauge-Natural, which has been mostly developed at the University of Turin (Italy) and at the Masaryk University in Brno (Czech Republic). In this framework, the group of automorphisms of some suitable principal bundle P, called the structure bundle, acts on fields by means of gauge transformations. After showing that the classical Wess-Zumino model can be consistently described within this formalism, we consider minimal supergravity (mSugra). We find that to embed mSugra in a Gauge-Natural framework, further investigations are needed. This happens since both the covariance of the Rarita-Schwinger Lagrangian and the closure of the SUSY algebra occur on-shell.