Open Superstring First Mass Level Effective Lagrangian: Massive Spin-3/2 Fields in an Electromagnetic Background

TL;DR

This paper derives explicit equations of motion and constraints for a charged massive spin-3/2 field in a constant electromagnetic background, based on the first massive level of open superstring theory.

Contribution

It provides a compact, explicit Lagrangian for the first massive level of open superstring, enabling straightforward derivation of equations of motion and constraints for spin-3/2 fields.

Findings

Explicit equations of motion for spin-3/2 fields in electromagnetic background

Two forms of Lagrangian: compact and decoupled system

Clarification of field coupling at the Lagrangian level

Abstract

We derive fully explicit equations of motion, and the associated set of constraints, describing the propagation in a flat space-time of a charged spin-3/2 massive state in a constant electromagnetic background. For this purpose, we provide the Lagrangian for the physical fermionic fields in the first massive level of the open superstring. We first write a compact Lagrangian, allowing a simple derivation of the equations of motion and constraints. Then another one is given that yields directly a decoupled system of equations, though the fields of different spins look coupled at the level of the Lagrangian.