Duality of a compact topological superconductor model and the Witten effect

Abstract

We consider a compact abelian Higgs model in 3+1 dimensions with a topological axion term and construct its dual theories for both bulk and boundary at strong coupling. The model may be viewed as describing a superconductor with magnetic monopoles, which can also be interpreted as a field theory of a topological Mott insulator. We show that this model is dual to a non-compact topological field theory of particles and vortices. It has exactly the same form of a model for superconducting cosmic strings with an axion term. We consider the duality of the boundary field theory at strong coupling and show that in this case $\theta$ is quantized as $-8\pi n/m$ where $n$ and $m$ are the quantum numbers associated to electric and magnetic charges. These topological states lack a non-interacting equivalent.

9.1 pages, 1 figure; v3: minor changes; references added; published version

References in corpus (9)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Axion topological field theory of topological superconductors
• Non-Meissner electrodynamics and knotted solitons in two-component superconductors
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Cited by in corpus (6)

• Fractional angular momentum at topological insulator interfaces
• Boson-fermion duality in a gravitational background
• Axion electrodynamics of Weyl superconductors with broken time-reversal symmetry
• Superselection Rules, Bosonization Duality in 1+1 Dimensions and Momentum-Space Entanglement
• Fermion-Vortex Interactions in Axion Electrodynamics
• Remarks on a compact Abelian Higgs model