A local action for fermionic unconstrained higher spin gauge fields in (A)dS space

TL;DR

This paper develops a local action principle for fermionic higher spin gauge fields in (A)dS space, extending previous bosonic results and connecting equations of motion to known higher spin equations.

Contribution

It introduces a fermionic higher spin action in (A)dS space, generalizing flat spacetime formulations and relating it to established higher spin equations.

Findings

Derived a fermionic higher spin action in (A)dS space.

Connected the action's equations of motion to Fronsdal and Fang-Fronsdal equations.

Extended flat spacetime fermionic theories to (A)dS backgrounds.

Abstract

The local free action principle for bosonic unconstrained higher spin gauge fields in $d$-dimensional (A)dS$_d$ spacetime has been already established by Segal. However, later on, Schuster and Toro, in 4-dimensional flat spacetime, extracted such an action from their bosonic continuous spin gauge theory, when the continuous spin parameter vanishes. On the other hand, similar to the Schuster-Toro's action, we found the fermionic continuous spin gauge theory in 4-dimensional flat spacetime. Thus it is noteworthy to take out its fermionic higher spin formulation in a limit, and generalize it to $d$-dimensional (A)dS$_d$ spacetime. Therefore, in this paper, we will present a similar action principle \`a la Segal for fermions in $d$-dimensional (A)dS$_d$ spacetime. Moreover, at the level of equations of motion, we will demonstrate how the Fronsdal and the Fang-Fronsdal equations in $d$-dimensional (A)dS$_d$ spacetime are related, respectively, to the Euler-Lagrange equations of the bosonic and fermionic higher spin actions mentioned above.