Chiral rings,singularity theory and electric-magnetic duality |
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| Institution: | 1. Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637, USA;2. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, 76100, Israel;3. Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855, USA;1. State Key Laboratory of Silkworm Genome Biology, College of Biotechnology, Southwest University, Chongqing, 400715, PR China;2. Institute for Clean Energy & Advanced Materials, Southwest University, Chongqing, 400715, PR China;3. College of Rongchang, Southwest University, Chongqing, 402460, PR China;1. Yau Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing, 100084, China;2. Department of Physics, POSTECH, Pohang 790-784, Republic of Korea;3. Asia Pacific Center for Theoretical Physics, POSTECH, Pohang 37673, Republic of Korea;4. Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea;1. Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, United Kingdom;2. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA;1. Department of Anesthesiology, Hospital Universitário Júlio Muller, Universidade Federal de Mato Grosso (UFMT), Cuiabá, MT, Brazil;2. Centro de Ensino e Treinamento da Sociedade Brasileira de Anestesiologia (CET/SBA), Cuiabá, MT, Brazil;3. Department of Gynecology and Obstetrics, Universidade Federal de Mato Grosso (UFMT), Cuiabá, MT, Brazil |
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| Abstract: | We study in detail the space of perturbations of a pair of dual N = 1 supersymmetric theories based on an SU(Nc) gauge theory with an adjoint X and fundamentals with a superpotential which is polynomial in X. The equivalence between them depends on non-trivial facts about polynomial equations, i.e. singularity theory. The classical chiral rings of the two theories are different. Quantum mechanically there are new relations in the chiral rings which ensure their equivalence. Duality interchanges “trivial” classical relations in one theory with quantum relations in the other and vice versa. We also speculate about the behavior of the theory without the superpotential. |
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