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

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 à 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.

arXiv comment24 pages. v3: Subsec. 2.4 was added. Abstract, introduction and conclusion improved to match the accepted version in PRD

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• Lagrangian BRST formulation of massive higher spin fields of generic symmetry type
• Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants