The Witten index in superspace,two-dimensional superanomaly in Yang-Mills and gravitational background,and superspace Schwinger-Dewitt heat kernel method |
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| Affiliation: | 1. Department of Biological Sciences, Gachon University, Seongnam, South Korea;2. Department of Bionanotechnology, Gachon University, Gyeonggi-do 13120, Republic of Korea;1. IMT Lille Douai, F-59000 Lille, France;2. University of Lille University of Seville, Spain;1. Institute for Agricultural and Fisheries Research (ILVO), Burg. Van Gansberghelaan 92, 9820 Merelbeke, Belgium;2. Research Group EnVOC, Department of Sustainable Organic Chemistry and Technology, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, 9000 Gent, Belgium;3. Department of Industrial Biological Sciences, Faculty of Bioscience Engineering, Ghent University, Graaf Karel de Goedelaan 5, 8500 Kortrijk, Belgium;4. Department of Agricultural Economics, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, 9000 Gent, Belgium |
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| Abstract: | We consider the Witten index in superspace and show that it is closely related to the superspace Schwinger-DeWitt heat kernel. By evaluating the Witten index for the two-dimensional superspace Yang-Mills and gravitational systems we obtain the two-dimensional superanomaly in an efficient way. Furthermore we show an effective way to treat the three-dimensional supersymmetric Yang-Mills system by the superspace Schwinger-DeWitt heat kernel method. As a consequence, the supersymmetric Chern-Simons term is obtained. |
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