Electromagnetic Interaction of Massive Spin-3 State from String Theory

TL;DR

Problem: how to consistently couple massive high-spin fields from string theory to a constant electromagnetic field. Approach: BRST quantization of the open boson string yields a gauge-invariant Lagrangian for the second massive level, containing spins $3$ and $1$, with a constant EM field inducing state mixing. Key contributions: explicit Lagrangian and gauge transformations showing EM-induced mixing of $s=3$ and $s=1$ at this level, plus field-redefinitions to isolate the pure $s=3$ sector and discussion of potential mixing at higher levels; extension to non-critical dimensions via an enlarged Fock space with scalar operators and parameter $\beta$, preserving BRST nilpotency. Significance: provides a concrete covariant framework for high-spin interactions in string theory under external fields and suggests systematic level mixing beyond the second massive level.

Abstract

In the given work we study an interaction of second massive state of an open boson string with the constant electromagnetic field. This state contains massive fields with spins 3 and 1. Using the method of an open string BRST quantization, we receive gauge-invariant lagrangian, describing the electromagnetic interaction of these fields. From the explicit view of transformations and lagrangian it follows that the presence of external constant e/m field leads to the mixing of the given level states. Most likely that the presence of the external field will lead to the mixing of the states at other mass string levels as well.