A Fresh Look at Generalized Veneziano Amplitudes

TL;DR

This paper revisits generalized Veneziano amplitudes, exploring their duality properties and demonstrating a ghost-free regime within certain deformations, advancing understanding of dual resonance models in string theory.

Contribution

It introduces a new regime within deformed Veneziano amplitudes where logarithmic trajectories remain ghost free, expanding the class of viable dual resonance models.

Findings

Identifies a ghost-free regime in deformed logarithmic Veneziano amplitudes

Demonstrates the existence of solutions satisfying duality constraints

Provides empirical evidence supporting extended amplitude solutions

Abstract

The dual resonance model, which was a precursor of string theory was based upon the idea that two-particle scattering amplitudes should be expressible equivalently as a sum of contributions of an infinite number of $s$ channel poles each corresponding to a finite number of particles with definite spin, or as a similar sum of $t$ channel poles. The famous example of Veneziano \cite{ven} satisfies all these requirements, and is additionally ghost free.We recall other trajectories which provide solutions to the duality constraints, e.g. the general Mobi\"us trajectories and the logarithmic trajectories, which were thought to be lacking this last feature. We however demonstrate, partly empirically, the existence of a regime within a particular deformation of the Veneziano amplitude for logarithmic trajectories for which the amplitude remains ghost free.