New Phenomenon of Nonlinear Regge Trajectory and Quantum Dual String Theory

TL;DR

This paper investigates a novel nonlinear Regge trajectory in a q-deformed dual string theory, revealing a square-root relation between spin and mass for specific deformation parameters, contrasting with traditional linear trajectories.

Contribution

It introduces a new nonlinear Regge trajectory arising from q-deformed string theory at roots of unity, showing a transition from linear to square-root behavior.

Findings

Regge trajectory becomes square-root for specific q values

Fock space truncation occurs at roots of unity

Spin-mass relation deviates from linear trajectory

Abstract

The relation between the spin and the mass of an infinite number of particles in a $q$-deformed dual string theory is studied. For the deformation parameter $q$ a root of unity, in addition to the relation of such values of $q$ with the rational conformal field theory, the Fock space of each oscillator mode in the Fubini-Veneziano operator formulation becomes truncated. Thus, based on general physical grounds, the resulting spin-(mass)$^2$ relation is expected to be below the usual linear trajectory. For such specific values of $q$, we find that the linear Regge trajectory turns into a square-root trajectory as the mass increases.