Revisiting Higher-Spin Gyromagnetic Couplings

TL;DR

This paper derives a universal formula for gyromagnetic couplings of massive string states in various string theories, confirming it through amplitude calculations and analyzing the gyromagnetic ratio for different states.

Contribution

It provides a general, universal expression for higher-spin gyromagnetic couplings in multiple string theories, validated by explicit amplitude computations.

Findings

Gyromagnetic ratio g=1 for states with zero Kaluza-Klein or Winding charges.

Derived a universal formula for string state couplings to gauge fields.

Analyzed gyromagnetic ratios for symmetric and mixed symmetry states.

Abstract

We analyze Bosonic, Heterotic, and Type II string theories compactified on a generic torus having constant moduli. By computing the hamiltonian giving the interaction between massive string excitations and $U(1)$ gauge fields arising from the graviton and Kalb-Ramond field upon compactification, we derive a general formula for such couplings that turns out to be universal in all these theories. We also confirm our result by explicitly evaluating the relevant string three-point amplitudes. From this expression, we determine the gyromagnetic ratio $g$ of massive string states coupled to both gauge-fields. For a generic mixed symmetry state, there is one gyromagnetic coupling associated with each row of the corresponding Young Tableau diagram. For all the states having zero Kaluza Klein or Winding charges, the value of $g$ turns out to be $1$. We also explicitly consider totally symmetric and mixed symmetry states (having two rows in the Young diagram) associated with the first Regge-trajectory and obtain their corresponding $g$ value.