Abstract
A correspondence is established between the dynamics of the two-vortex system and the non-commutative Landau problem (NCLP) in its sub- (non-chiral), super- (chiral) and critical phases. As a result, a trivial permutation symmetry of the point vortices induces a weak-strong coupling duality in the NCLP. We show that quantum two-vortex systems with non-zero total vorticity can be generated by applying conformal bridge transformation to a two-dimensional quantum free particle or to a quantum vortex-antivortex system of zero total vorticity. The sub- and super-critical phases of the quantum NCLP are generated in a similar way from the 2D quantum free particle in a commutative or non-commutative plane. The composition of the inverse and direct transformations of the conformal bridge also makes it possible to link the non-chiral and chiral phases in each of these two systems.
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Acknowledgments
The work was partially supported by the FONDECYT Project 1190842 and the DICYT Project 042331PS−Ayudante. We thank J. Gamboa and L. Inzunza for useful discussions.
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Alcala, A., Plyushchay, M.S. Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation. J. High Energ. Phys. 2023, 141 (2023). https://doi.org/10.1007/JHEP08(2023)141
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DOI: https://doi.org/10.1007/JHEP08(2023)141