`` Rerum Universitas Sententia ex Susy'' (A View of the Universe according to Supersymmetry)

TL;DR

This paper investigates the feasibility of defining conserved currents in supersymmetric minisuperspaces using direct differential equations from quantum constraints, finding limited success except in simple cases.

Contribution

It demonstrates that conserved currents in supersymmetric minisuperspaces can only be consistently defined in very simple scenarios, using equations derived from the supersymmetric algebra.

Findings

Conserved currents are generally not definable in complex supersymmetric minisuperspaces.

Simple scenarios allow for conserved currents derived directly from quantum constraints.

The approach relies on Wheeler-DeWitt like equations from supersymmetric algebra.

Abstract

The question if conserved currents can be sensibly defined in supersymmetric minisuperspaces is investigated in this essay. The objective is to employ exclusively the differential equations obtained {\em directly} from the Lorentz and supersymmetry quantum constraints. The ``square-root'' structure of N=1 supergravity is the motivation to contemplate this tempting idea. However, it is shown that such prospect is not feasible but for some very simple scenarios. Otherwise, conserved currents (and consistent probability densities) can be derived from subsequent Wheeler-DeWitt like equations obtained from the supersymmetric algebra of constraints.