Reality of Complex Affine Toda Solitons

TL;DR

This paper investigates the reality conditions of complex affine Toda solitons, revealing that only a limited subset of solutions meet the reality and positivity constraints, impacting their physical relevance.

Contribution

It introduces a simple pairing condition that determines which complex affine Toda solitons have real energy density and discusses their physical implications.

Findings

Few soliton solutions satisfy the reality constraint.

Positivity further restricts the set of physical solutions.

The reality condition is linked to a pairing condition.

Abstract

There are infinitely many topological solitons in any given complex affine Toda theories and most of them have complex energy density. When we require the energy density of the solitons to be real, we find that the reality condition is related to a simple ``pairing condition.'' Unfortunately, rather few soliton solutions in these theories survive the reality constraint, especially if one also demands positivity. The resulting implications for the physical applicability of these theories are briefly discussed.