Bosonic string massive scalar amplitudes and absence of "chaos''

TL;DR

This paper computes various four-point massive scalar amplitudes in bosonic string theory, demonstrating their regularity and exploring the absence of chaotic behavior, with insights into the spectrum and null state complications.

Contribution

It provides explicit covariant calculations of massive scalar amplitudes up to level 11 and offers a simple model explaining their regularity, addressing null state issues with a novel gauge.

Findings

All computed amplitudes are regular and show no signs of chaos.

The null state complications can be managed using a new gauge that clarifies spin degeneracy.

Explicit calculations up to level 11 confirm the theoretical expectations.

Abstract

We compute directly in covariant formalism various four point massive scalar amplitudes in bosonic string with scalars up to level 11. The most ``difficult'' amplitude we consider is four identical scalars at level 4, i.e. the first non trivial amplitude with four identical massive scalars. All other amplitudes have at least one tachyon. All computed amplitudes are perfectly regular and show no sign of erratic behavior. While this could be naively expected it is not completely trivial because of higher spins exchanged. We give a naive argument based on a very simple model of why this can reasonably be expected and we check on the explicit examples that the intuition derived from the model is sensible. Furthermore we discuss the complications due to null states (BRST exact states) in actually computing the covariant bosonic string spectrum and how these can be overcome by using a ``$\Pi$ gauge'' which makes manifest that the degeneration of any spin at any mass level is independent on the spacetime dimension as predicted by Curtright et al at the end of 90s.