# Fermionic continuous spin gauge field in (A)dS space

## TL;DR

This paper develops a gauge-invariant Lagrangian formulation for fermionic continuous spin fields in (A)dS space, demonstrating their properties, gauge symmetries, and decoupling limits to various fermionic fields.

## Contribution

It introduces a novel Lagrangian formulation for fermionic continuous spin fields in (A)dS space using gamma-traceless tensor-spinor fields and explores their gauge symmetries and limits.

## Key findings

- Partition function of the fermionic continuous spin field equals one.
- A modified de Donder gauge simplifies equations of motion.
- Decoupling limits yield massless, partial-massless, and massive fermionic fields.

## Abstract

Fermionic continuous spin field propagating in (A)dS space-time is studied. Gauge invariant Lagrangian formulation for such fermionic field is developed. Lagrangian of the fermionic continuous spin field is constructed in terms of triple gamma-traceless tensor-spinor Dirac fields, while gauge symmetries are realized by using gamma-traceless gauge transformation parameters. It is demonstrated that partition function of fermionic continuous spin field is equal to one. Modified de Donder gauge condition that considerably simplifies analysis of equations of motion is found. Decoupling limits leading to arbitrary spin massless, partial-massless, and massive fermionic fields are studied.