Emergent vortex-electron interaction from dualization

Shantonu Mukherjee; Amitabha Lahiri

doi:10.1016/j.aop.2020.168167

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arXiv · 1912.03124

Emergent vortex-electron interaction from dualization

Shantonu Mukherjee·Amitabha Lahiri

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Abstract

We consider the Abelian Higgs model in 3+1 dimensions with vortex lines, into which charged fermions are introduced. This could be viewed as a model of a type-II superconductor with unpaired electrons (or holes), analogous to the boson-fermion model of high-$T_c$ superconductors but one in which the bosons and fermions interact only through the electromagnetic gauge field. We investigate the dual formulation of this model, which is in terms of a massive antisymmetric tensor gauge field $B_{μν}$ mediating the interaction of the vortex lines. This field couples to the fermions through a nonlocal spin-gauge interaction term. We then calculate the quantum correction due to the fermions at one loop and show that due to the presence of this new nonlocal term a topological $B \wedge F$ interaction is induced in the effective action, leading to an increase in the mass of both the photon and the tensor gauge field. Additionally, we find a Coulomb potential between the electrons, but with a large dielectric constant generated by the one-loop effects.

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Shantonu Mukherjee, Amitabha Lahiri. 2020-04-14. Emergent vortex-electron interaction from dualization. https://doi.org/10.1016/j.aop.2020.168167

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