Accumulation-Point Amplitudes in String Theory

TL;DR

This paper compares the Coon amplitude and open string scattering in AdS, highlighting their spectral similarities and differences, and suggests a possible string background realization for the Coon amplitude.

Contribution

It identifies common qualitative features between the Coon amplitude and open string amplitudes in AdS, proposing a potential string background for the Coon amplitude.

Findings

Both amplitudes share an accumulation point in their spectra.

They exhibit similar high-energy fixed-angle behavior.

Differences are observed in the spectrum of states with highest angular momentum.

Abstract

We point out some common qualitative features of the Coon amplitude$\unicode{x2014}$a family of deformations of the Veneziano amplitude with logarithmic Regge trajectories$\unicode{x2014}$and the open string scattering amplitude for strings ending on a D-brane in AdS. Both reduce to the Veneziano amplitude at relatively low energies. Both systems have an accumulation point in their spectrum, with an infinite number of states below a certain energy. The approach to this point is very similar. Both have the same high-energy fixed-angle behavior. Nevertheless, we find some differences in the spectrum of states with highest angular momentum. These similarities suggest that there may exist a string background that realizes the Coon amplitude.