Quantum Bound States in Yang-Mills-Higgs Theory

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Boulton, Lyonell, Schroers, Bernd J, Smedley-Williams, Kim
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.08.2018
Subjects
Eigenvalues
Galerkin method
Laplace transforms
Linear operators
Linearization
Mathematical analysis
Mathematics - Mathematical Physics
Monopoles
Physics - High Energy Physics - Theory
Physics - Mathematical Physics
Upper bounds
Yang-Mills theory
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1708.08363