String Theory and The Velo-Zwanziger Problem

TL;DR

This paper investigates how string theory's high-spin states behave in electromagnetic fields, demonstrating that string theory avoids causality issues seen in traditional field theories and analyzing spectrum properties and critical factors.

Contribution

It generalizes Fierz-Pauli conditions for string states, showing string theory bypasses the Velo-Zwanziger causality problem and discusses spectrum and background effects.

Findings

String theory's high-spin states maintain causality in electromagnetic backgrounds.

Open-string spectrum remains ghost-free in weak constant fields.

First Regge trajectory can be isolated and described consistently.

Abstract

We examine the behavior of the leading Regge trajectory of the open bosonic string in a uniform electromagnetic background and present a consistent set of Fierz-Pauli conditions for these symmetric tensors that generalizes the Argyres-Nappi spin-2 result. These equations indicate that String Theory does bypass the Velo-Zwanziger problem, i.e. the loss of causality experienced by a massive high-spin field minimally coupled to electromagnetism. Moreover, we provide some evidence that only the first Regge trajectory can be described in isolation and show that the open-string spectrum is free of ghosts in weak constant backgrounds. Finally, we comment on the roles of the critical dimension and of the gyromagnetic ratio.