Particle-vortex and Maxwell duality in the $Ad{S}_4\times {\mathbb{CP}}^3$/ABJM correspondence

Abstract

We revisit the notion of particle-vortex duality in abelian theories of complex scalar fields coupled to gauge fields, formulating the duality as a transformation at the level of the path integral. This transformation is then made symmetric and cast as a self-duality that maps the original theory into itself with the role of particles and vortices interchanged. After defining the transformation for a pure Chern-Simons gauge theory, we show how to embed it into (a sector of) the $(2+1)-$dimensional ABJM model, and argue that this duality can be understood as being related to 4-dimensional Maxwell duality in the $Ad{S}_4\times {\mathbb{CP}}^3$ bulk.

arXiv comment29 pages

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