Instability of Solitons in imaginary coupling affine Toda Field Theory

TL;DR

This paper investigates the classical and quantum stability of solitons in imaginary coupling affine Toda field theory, revealing that many classical solutions are unstable due to finite-time singularities, challenging previous stability assumptions.

Contribution

It demonstrates the existence of unstable classical solutions with finite-time singularities, questioning earlier stability claims and emphasizing the need for a more rigorous quantum formulation.

Findings

Many classical solutions develop singularities after finite time

Previous stability claims ignored these unstable solutions

A more rigorous quantum framework is necessary

Abstract

Affine Toda field theory with a pure imaginary coupling constant is a non-hermitian theory. Therefore the solutions of the equation of motion are complex. However, in $1+1$ dimensions it has many soliton solutions with remarkable properties, such as real total energy/momentum and mass. Several authors calculated quantum mass corrections of the solitons by claiming these solitons are stable. We show that there exists a large class of classical solutions which develops singularity after a finite lapse of time. Stability claims, in earlier literature, were made ignoring these solutions. Therefore we believe that a formulation of quantum theory on a firmer basis is necessary in general and for the quantum mass corrections of solitons, in particular.