Noether superpotentials in supergravities

TL;DR

This paper addresses the correct derivation of superpotentials in supergravity theories, correcting previous methods and confirming the results through Hamiltonian formalism, with implications for understanding supercharges and algebra extensions.

Contribution

It introduces a Lagrangian-based criterion to derive the correct superpotential in supergravity, resolving issues with the standard Noether method.

Findings

Correct superpotential derived using Lagrangian methods

Verification of equivalence with Hamiltonian formalism

Re-derivation of magnetic charge extension in supergravity algebra

Abstract

Straightforward application of the standard Noether method in supergravity theories yields an incorrect superpotential for local supersymmetry transformations, which gives only half of the correct supercharge. We show how to derive the correct superpotential through Lagrangian methods, by applying a criterion proposed recently by one of us. We verify the equivalence with the Hamiltonian formalism. It is also indicated why the first-order and second-order formalisms lead to the same superpotential. We rederive in particular the central extension by the magnetic charge of the ${\cal N}_4 =2$ algebra of SUGRA asymptotic charges.