On the off-shell superfield Lagrangian formulation of $4D$, $\mathcal{N}{=}\,1$ supersymmetric infinite spin theory

TL;DR

This paper develops a complete off-shell Lagrangian formulation for 4D, N=1 supersymmetric infinite spin theory, introducing superfields and demonstrating consistency with previous component formulations.

Contribution

It provides the first off-shell superfield Lagrangian description of 4D, N=1 supersymmetric infinite spin theory, extending the component approach to a superfield framework.

Findings

Superfield Lagrangian constructed in terms of chiral and antichiral superfields.

Component form of superfield Lagrangian matches previous component results.

Fields form six infinite spin supermultiplets extended to superfields.

Abstract

We develop a complete off-shell Lagrangian description of the free $4D, {\cal N}=1$ supersymmetric theory of infinite spin. Bosonic and fermionic fields are formulated in terms of spin-tensor fields with dotted and undotted indices. The corresponding Lagrangians for bosonic and fermionic infinite spin fields entering into the on-shell supersymmetric model are derived within the BRST method. Lagrangian for this supersymmetric model is written in terms of the complex infinite spin bosonic field and infinite spin fermionic Weyl field subject to supersymmetry transformations. The fields involved into the on-shell supersymmetric Lagrangian can be considered as components of six infinite spin chiral and antichiral multiplets. These multiplets are extended to the corresponding infinite spin chiral and antichiral superfields so that two chiral and antichiral superfields contain among the components the basic fields of an infinite spin supermultiplet and extra four chiral and antichiral superfields containing only the auxiliary fields needed for the Lagrangian formulation. The superfield Lagrangian is constructed in terms of these six chiral and antichiral supefields, and we show that the component form of this superfield Lagrangian exactly coincides with the previously found component supersymmetric Lagrangian after eliminating the component fields added to construct (anti)chiral superfields.