Frame- and Metric-like Higher-Spin Fermions

TL;DR

This paper reviews and clarifies the two main formulations of higher-spin fermionic gauge fields, demonstrating their equivalence in free Anti-de Sitter space and discussing potential issues in interactions.

Contribution

It provides a detailed comparison of frame-like and metric-like formulations of higher-spin fermions, highlighting their equivalence and addressing subtleties in interactions.

Findings

Gauge-invariant Lagrangian for frame-like fermions in AdS space

Equivalence of the two formulations at the free level

Discussion of interaction-related subtleties

Abstract

Conventional descriptions of higher-spin fermionic gauge fields appear in two varieties: the Aragone-Deser-Vasiliev frame-like formulation and the Fang-Fronsdal metric-like formulation. We review, clarify and elaborate on some essential features of these two. For frame-like free fermions in Anti-de Sitter space, one can present a gauge-invariant Lagrangian description such that the constraints on the field and the gauge parameters mimic their flat-space counterparts. This simplifies the explicit demonstration of the equivalence of the two formulations at the free level. We comment on the subtleties that may arise in an interacting theory.