Power-law Behavior of High Energy String Scatterings in Compact Spaces

TL;DR

This paper investigates high energy string scattering in compact spaces, revealing a transition from exponential to power-law behavior linked to T-duality, and identifies conditions where linear relations among amplitudes break down.

Contribution

It uncovers the conditions under which high energy string scattering amplitudes shift from exponential to power-law behavior in compactified spaces, highlighting the role of T-duality.

Findings

Linear relations among amplitudes hold in some regimes.

Power-law behavior emerges when linear relations break down.

T-duality symmetry influences scattering amplitude behavior.

Abstract

We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. We obtain infinite linear relations among high energy scattering amplitudes. For some kinematic regimes, we discover that some linear relations break down and, simultaneously, the amplitudes enhance to power-law behavior due to the space-time T-duality symmetry in the compact direction. This result is consistent with the coexistence of the linear relations and the softer exponential fall-off behavior of high energy string scattering amplitudes as we pointed out prevously. It is also reminiscent of hard (power-law) string scatterings in warped spacetime proposed by Polchinski and Strassler.