Toda Soliton Mass Corrections and the Particle--Soliton Duality Conjecture

TL;DR

This paper calculates quantum corrections to soliton masses in affine Toda theories, providing evidence for a duality between solitons and fundamental particles that parallels S-duality in quantum field theories.

Contribution

It demonstrates that soliton mass ratios in affine Toda theories with imaginary exponentials renormalize similarly to particle ratios, supporting a quantum-level soliton-particle duality conjecture.

Findings

Soliton mass ratios renormalize nontrivially.

Evidence for quantum soliton-particle duality.

Supports the Toda theory duality as an S-duality toy model.

Abstract

We compute quantum corrections to soliton masses in affine Toda theories with imaginary exponentials based on the nonsimply-laced Lie algebras $c_n^{(1)}$. We find that the soliton mass ratios renormalize nontrivially, in the same manner as those of the fundamental particles of the theories with real exponentials based on the nonsimply-laced algebras $b_n^{(1)}$. This gives evidence that the conjectured relation between solitons in one Toda theory and fundamental particles in a dual Toda theory holds also at the quantum level. This duality can be seen as a toy model for S-duality.