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

TL;DR

This paper derives two explicit Lagrangians for the first massive spin-2 states in open superstring theory in four dimensions, addressing causality issues in electromagnetic backgrounds and providing tools for further theoretical investigations.

Contribution

It presents two related, explicit Lagrangian formulations for massive spin-2 string states, improving understanding of their dynamics in electromagnetic backgrounds.

Findings

Two explicit Lagrangians related by field redefinitions.

One reduces to Fierz-Pauli in absence of electromagnetic field.

A more compact form simplifies equations of motion and constraints.

Abstract

Minimal coupling leads to problems such as loss of causality if one wants to describe charged particles of spin greater than one propagating in a constant electromagnetic background. Regge trajectories in string theory contain such states, so their study may allow us to investigate possible avenues to remedy the pathologies. We present here two explicit forms, related by field redefinitions, of the Lagrangian describing the bosonic states in the first massive level of open superstrings in four dimensions. The first one reduces, when the electromagnetic field is set to zero, to the Fierz-Pauli Lagrangian for the spin-2 mode. The second one is a more compact form which simplifies the derivation of a Fierz-Pauli system of equations of motion and constraints.