Notes on High Energy Limit of Bosonic Closed String Scattering Amplitudes

TL;DR

This paper investigates high-energy bosonic closed string scattering amplitudes, clarifies saddle-point calculation issues, and uses KLT relations to derive new amplitude results, revealing discrepancies with previous findings.

Contribution

It demonstrates the persistence of high-energy constraints for closed strings, clarifies saddle-point calculation limitations, and provides corrected high-energy amplitude formulas using KLT relations.

Findings

Saddle-point method is unreliable for closed string amplitudes.

High-energy constraints from zero-norm states apply to closed strings.

New amplitude results differ from previous Gross-Mende calculations.

Abstract

We study bosonic closed string scattering amplitudes in the high-energy limit. We find that the methods of decoupling of high-energy zero-norm states and the high-energy Virasoro constraints, which were adopted in the previous works to calculate the ratios among high-energy open string scattering amplitudes of different string states, persist for the case of closed string. However, we clarify the previous saddle-point calculation for high-energy open string scattering amplitudes and claim that only (t,u) channel of the amplitudes is suitable for saddle-point calculation. We then discuss three evidences to show that saddle-point calculation for high-energy closed string scattering amplitudes is not reliable. By using the relation of tree-level closed and open string scattering amplitudes of Kawai, Lewellen and Tye (KLT), we calculate the high-energy closed string scattering amplitudes for arbitrary mass levels. For the case of high-energy closed string four-tachyon amplitude, our result differs from the previous one of Gross and Mende, which is NOT consistent with KLT formula, by an oscillating factor.