Particle-vortex and Maxwell duality in the $AdS_4\times \mathbb{CP}^3$/ABJM correspondence

TL;DR

This paper explores a particle-vortex duality in abelian theories and connects it to Maxwell duality within the $AdS_4\times \mathbb{CP}^3$/ABJM framework, revealing a self-duality structure in the theory.

Contribution

It formulates a symmetric particle-vortex duality as a path integral transformation and embeds it into the ABJM model, linking it to Maxwell duality in the $AdS_4$ bulk.

Findings

Established a self-duality mapping in abelian gauge theories.

Embedded the duality into the ABJM model.

Connected the particle-vortex duality to Maxwell duality in $AdS_4$.

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 $AdS_{4}\times\mathbb{CP}^{3}$ bulk.