Quantum Bound States in Yang-Mills-Higgs Theory

TL;DR

This paper proves the existence of infinitely many bound states in Yang-Mills-Higgs theory for specific operators and explores their spectral properties, providing insights into electric-magnetic duality.

Contribution

It provides rigorous proofs for bound states in Yang-Mills-Higgs equations and analyzes spectral similarities related to duality conjectures.

Findings

Existence of infinitely many bound states for specific operators.

Computed upper bounds on the lowest 20 eigenvalues.

Identified spectral similarities supporting duality conjectures.

Abstract

We give rigorous proofs for the existence of infinitely many (non-BPS) bound states for two linear operators associated with the Yang-Mills-Higgs equations at vanishing Higgs self-coupling and for gauge group SU(2): the operator obtained by linearising the Yang-Mills-Higgs equations around a charge one monopole and the Laplace operator on the Atiyah-Hitchin moduli space of centred charge two monopoles. For the linearised system we use the Riesz-Galerkin approximation to compute upper bounds on the lowest 20 eigenvalues. We discuss the similarities in the spectrum of the linearised system and the Laplace operator, and interpret them in the light of electric-magnetic duality conjectures.