# Lagrangian formulation of the massive higher spin N=1 supermultiplets in $AdS_4$ space

## TL;DR

This paper constructs explicit Lagrangians for massive higher spin N=1 supermultiplets in AdS4, using a gauge-invariant frame-like approach, and derives supertransformations that preserve the combined Lagrangian structure.

## Contribution

It provides the first explicit component Lagrangian formulation of massive higher spin supermultiplets in AdS4 with on-shell supersymmetry transformations.

## Key findings

- Supertransformations leave the combined Lagrangian invariant.
- Superalgebra closes on-shell for the constructed supermultiplets.
- Explicit gauge-invariant Lagrangian for massive higher spin supermultiplets.

## Abstract

We give an explicit component Lagrangian construction of massive higher spin on-shell $N=1$ supermultiplets in four-dimensional Anti-de Sitter space $AdS_4$. We use a frame-like gauge invariant description of massive higher spin bosonic and fermionic fields. For the two types of the supermultiplets (with integer and half-integer superspins) each one containing two massive bosonic and two massive fermionic fields we derive the supertransformations leaving the sum of four their free Lagrangians invariant such that the algebra of these supertransformations is closed on-shell.

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Source: https://tomesphere.com/paper/1901.09637