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 AdS4 × ℂℙ3 bulk.
E. Witten and D.I. Olive, Supersymmetry Algebras That Include Topological Charges, Phys. Lett. B 78 (1978) 97 [INSPIRE].
A. Zee, Quantum Field Theory in a nutshell, second edition, Princeton University Press, (2010).
D.H. Lee and M.P.A. Fisher, Anyon superconductivity and charge vortex duality, Int. J. Mod. Phys. B 5 (1991) 2675 [INSPIRE].
S. Sachdev and X. Yin, Quantum phase transitions beyond the Landau-Ginzburg paradigm and supersymmetry, Annals Phys. 325 (2010) 2 [INSPIRE].
X. Chu, H. Nastase, B.E.W. Nilsson and C. Papageorgakis, Higgsing M2 to D2 with gravity: N =6 chiral supergravity from topologically gauged ABJM theory, JHEP 04 (2011) 040 [arXiv:1012.5969] [INSPIRE].
A. Mohammed, J. Murugan and H. Nastase, Towards a Realization of the Condensed-Matter/Gravity Correspondence in String Theory via Consistent Abelian Truncation, Phys. Rev. Lett. 109 (2012) 181601 [arXiv:1205.5833] [INSPIRE].
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
ArXiv ePrint: 1404.5926
About this article
Cite this article
Murugan, J., Nastase, H., Rughoonauth, N. et al. Particle-vortex and Maxwell duality in the AdS4 × ℂℙ3/ABJM correspondence. J. High Energ. Phys. 2014, 51 (2014). https://doi.org/10.1007/JHEP10(2014)051
- Duality in Gauge Field Theories
- Solitons Monopoles and Instantons
- AdS-CFT Correspondence