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Existence Theorems for Vortices in the Aharony–Bergman–Jaferis–Maldacena Model

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Abstract

A series of sharp existence and uniqueness theorems are established for the multiple vortex solutions in the supersymmetric Chern–Simons–Higgs theory formalism of Aharony, Bergman, Jaferis, and Maldacena, for which the Higgs bosons and Dirac fermions lie in the bifundamental representation of the general gauge symmetry group \({U(N)\times U(N)}\). The governing equations are of the BPS type and derived by Kim, Kim, Kwon, and Nakajima in the mass-deformed framework labeled by a continuous parameter.

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Authors and Affiliations

  1. Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University, Kaifeng, 475004, Henan, People’s Republic of China

    Xiaosen Han

  2. Department of Mathematics, Polytechnic School, New York University, Brooklyn, NY, 11201, USA

    Yisong Yang

  3. NYU-ECNU Institute of Mathematical Sciences, New York University, Shanghai, 3663 North Zhongshan Road, Shanghai, 200062, People’s Republic of China

    Yisong Yang

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  1. Xiaosen Han
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Correspondence to Yisong Yang.

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Communicated by N. A. Nekrasov

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Han, X., Yang, Y. Existence Theorems for Vortices in the Aharony–Bergman–Jaferis–Maldacena Model. Commun. Math. Phys. 333, 229–259 (2015). https://doi.org/10.1007/s00220-014-2179-6

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  • DOI: https://doi.org/10.1007/s00220-014-2179-6

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