# Lagrangian formulation for the infinite spin N=1 supermultiplets in d=4

## TL;DR

This paper constructs an explicit Lagrangian for massless infinite spin N=1 supermultiplets in four-dimensional Minkowski space, detailing their gauge invariance and supertransformation algebra.

## Contribution

It provides the first explicit Lagrangian formulation for massless infinite spin supermultiplets in 4D Minkowski space, including supertransformations and algebra closure.

## Key findings

- Supertransformations leave the combined Lagrangian invariant.
- Superalgebra closes on-shell.
- Explicit gauge-invariant Lagrangians derived for infinite spin fields.

## Abstract

We provide an explicit Lagrangian construction for the massless infinite spin N=1 supermultiplet in four dimensional Minkowski space. Such a supermultiplet contains a pair of massless bosonic and a pair of massless fermionic infinite spin fields with properly adjusted dimensionful parameters. We begin with the gauge invariant Lagrangians for such massless infinite spin bosonic and fermionic fields and derive the supertransformations which leave the sum of their Lagrangians invariant. It is shown that the algebra of these supertransformations is closed on-shell.