Quantum mass corrections for affine Toda solitons

TL;DR

This paper computes the first quantum corrections to soliton masses in affine Toda theories, revealing that classical mass relationships hold for simply-laced and twisted cases but not straightforwardly for non-simply-laced cases.

Contribution

It provides the first semi-classical quantum mass correction calculations for affine Toda solitons across different algebra classes.

Findings

Classical mass relationships persist for simply-laced and twisted cases.

Naive classical relationships do not hold for non-simply-laced cases.

Quantum corrections vary depending on the algebra class.

Abstract

We calculate the first quantum corrections to the masses of solitons in imaginary-coupling affine Toda theories using the semi-classical method of Dashen, Hasslacher and Neveu. The theories divide naturally into those based on the simply-laced, the twisted and the untwisted non-simply-laced algebras. We find that the classical relationships between soliton and particle masses found by Olive {\em et al.\ }persist for the first two classes, but do not appear to do so naively for the third.