Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields

TL;DR

This paper develops a framework for fermionic higher-spin gauge fields in four dimensions using three-dimensional prepotentials with conformal symmetry, extending previous bosonic theories and revealing a unified action structure.

Contribution

It introduces fermionic prepotentials in four-dimensional higher-spin theories, generalizing bosonic results and establishing a unified action formulation across spins.

Findings

Prepotentials exhibit higher-spin diffeomorphism and Weyl symmetries.

Equations of motion reformulated as twisted self-duality conditions.

Hamiltonian constraints explicitly solved in terms of prepotentials.

Abstract

We introduce prepotentials for fermionic higher-spin gauge fields in four spacetime dimensions, generalizing earlier work on bosonic fields. To that end, we first develop tools for handling conformal fermionic higher-spin gauge fields in three dimensions. This is necessary because the prepotentials turn out to be three-dimensional fields that enjoy both "higher-spin diffeomorphism" and "higher-spin Weyl" gauge symmetries. We discuss a number of the key properties of the relevant Cotton tensors. The reformulation of the equations of motion as "twisted self-duality conditions" is then exhibited. We show next how the Hamiltonian constraints can be explicitly solved in terms of appropriate prepotentials and show that the action takes then the same remarkable form for all spins.