Comments on the high energy limit of bosonic open string theory

TL;DR

This paper refines the derivation of high-energy scattering amplitude ratios in bosonic open string theory, reducing assumptions and providing new perspectives using decoupling of spurious states and DDF states.

Contribution

It weakens the assumptions needed for deriving amplitude ratios and introduces a DDF state perspective to understand high-energy behavior.

Findings

Reduced the assumption from momentum to longitudinal polarization approximation.

Verified the new assumption using saddle-point approximation for specific cases.

Showed that only one independent high-energy amplitude exists per mass level using DDF states.

Abstract

In previous works, ratios among four-point scattering amplitudes at the leading order in the high-energy limit were derived for the bosonic open string theory. The derivation was based on Ward identities derived from the decoupling of zero-norm states and was purely algebraic. The only assumption of the derivation was that the momentum polarization can be approximated by the longitudinal polarization at high energies. In this paper, using the decoupling of spurious states, we reduce this assumption to a much weaker one which can be easily verified by simple power counting in most cases. For the special cases which are less obvious, we verify the new assumption for an example by saddle-point approximation. We also provide a new perspective to our previous results in terms of DDF states. In particular, we show that, by using DDF states, one can easily see that there is only one independent high energy scattering amplitude for each fixed mass level.