Linear Relations and their Breakdown in High Energy Massive String Scatterings in Compact Spaces

TL;DR

This paper investigates high energy scattering amplitudes of compactified closed bosonic strings, revealing linear relations among amplitudes and their breakdown in certain regimes, leading to power-law behavior influenced by T-duality symmetry.

Contribution

It uncovers the conditions under which linear relations among high energy string scattering amplitudes break down, resulting in a transition to power-law behavior influenced by T-duality.

Findings

Linear relations among scattering amplitudes are established for fixed mass levels.

Breakdown of linear relations occurs in specific kinematic regimes with N_{R}=N_{L}.

Amplitudes exhibit power-law behavior instead of exponential fall-off in certain regimes.

Abstract

We calculate high energy massive scattering amplitudes of closed bosonic string compactified on the torus. For each fixed mass level with given quantized and winding momenta ((m/R),(1/2)nR), we obtain infinite linear relations among high energy scattering amplitudes of different string states. For some kinematic regimes, we discover that linear relations with N_{R}=N_{L} break down and, simultaneously, the amplitudes enhance to power-law behavior instead of the usual expoential fall-off behavior at high energies. It is the space-time T-duality symmetry that plays a role here. 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 our previous work on the power-law behavior of high energy string/domain-wall scatterings.