Higgs bundles and four manifolds |
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| Institution: | 2. Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands;1. Center for Depression Research and Clinical Care, UT Southwestern Medical Center, Dallas, TX, United States;2. Department of Psychiatry, Icahn School of Medicine at Mount Sinai, New York, NY, United States;3. Quantitative Biomedical Research Center, Department of Population and Data Sciences, UT Southwestern Medical Center, Dallas, TX, United States;4. Department of Psychiatry, UT Southwestern Medical Center, Dallas, TX, United States;5. Department of Psychiatry, Texas Tech University Health Science Center, El Paso, Texas, United States;1. Department of Chemical Engineering, The University of Melbourne, Parkville, VIC, 3010, Australia;2. Department of Chemical Engineering, Faculty of Engineering, Monash University, Clayton, VIC, 3800, Australia;1. CERN, CH-1211 Genève 23, Switzerland;2. Physics Department, University of Connecticut, Storrs, CT 06269-3046, USA;3. RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA;4. Institut de Théorie des Phénomènes Physiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland |
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| Abstract: | It is known that the Seiberg–Witten invariants, derived from supersymmetric Yang–Mill theories in four dimensions, do not distinguish smooth structure of certain non-simply-connected four manifolds. We propose generalizations of Donaldson–Witten and Vafa–Witten theories on a Kähler manifold based on Higgs bundles. We showed, in particular, that the partition function of our generalized Vafa–Witten theory can be written as the sum of contributions our generalized Donaldson–Witten invariants and generalized Seiberg–Witten invariants. The resulting generalized Seiberg–Witten invariants might have, conjecturally, information on smooth structure beyond the original Seiberg–Witten invariants for non-simply-connected case. |
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