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) x CP3 bulk.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)National Research Foundation (NRF) of South AfricaDAAD-AIMS ScholarshipDAADUniv Cape Town, Dept Math & Appl Math, Lab Quantum Grav & Strings, ZA-7700 Rondebosch, South AfricaUniv Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, BrazilUniv Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, BrazilCNPq: 301219/2010-9FAPESP: 13/14152-7