Determinant formula for the topological N = 2 superconformal algebra |
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| Affiliation: | 1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK;2. Instituto de Matemáticas y Física Fundamental, CSIC, Serrano 123, Madrid 28006, Spain;3. NIKHEF-H, Kruislaan 409, NL-1098 SJ Amsterdam, The Netherlands;1. Key Laboratory of Ion Beam Bioengineering and Bioenergy Forest Research Center of State Forestry Administration, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, Anhui, PR China;2. School of Life Sciences, University of Science and Technology of China, Hefei 230027, Anhui, PR China;3. College of Food and Bioengineering, Henan University of Science and Technology, Luoyang 471023, Henan, PR China;1. Department of Physics, Boğaziçi University, Istanbul, Turkey;2. Department of Physics and Astronomy, University of Bonn, Bonn, Germany;3. Feza Gürsey Center for Physics and Mathematics, Boğaziçi University, Istanbul, Turkey;4. SISSA, via Bonomea 265, 34136 Trieste, Italy;5. INFN, Sezione di Trieste, Italy;6. IGAP, via Beirut 2/1, 34151 Trieste, Italy;7. ITEP, Bolshaya Cheremushkinskaya street 25, 117218 Moscow, Russia;8. ITMP MSU, Leninskie gory 1, 119991 Moscow, Russia;1. Faculty of Biology, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany;2. Faculty of Mathematics, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany;3. Faculty of Physics, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany;1. CNRS, Laboratoire de Mathématiques, Université de Reims-Champagne-Ardenne, FR 3399 CNRS, F-51687, Reims, France;2. Pennsylvania State University, Department of Mathematics, University Park, PA 16802, USA;3. ICERM, Brown University, Box1995, Providence, RI 02912, USA;1. Department of Stomatology, the 7th Medical Center of Chinese PLA General Hospital, 100700, Beijing, 100700, PR China;2. Outpatient Department of PLA Macao Garrison, Macao, 999078, PR China;3. State Key Laboratory of Military Stomatology and National Clinical Research Center for Oral Diseases and Shaanxi Clinical Research Center for Oral Diseases, Department of Orthodontics, School of Stomatology, The Fourth Military Medical University, Xi''an 710032, PR China;4. State Key Laboratory of Military Stomatology & National Clinical Research Center for Oral Diseases & Shaanxi Key Laboratory of Oral Diseases, Department of Prosthodontics, School of Stomatology, The Fourth Military Medical University, Xi’an, 710032, PR China |
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| Abstract: | ![]()
The Kac determinant for the topological N = 2 superconformal algebra is presented as well as a detailed analysis of the singular vectors detected by the roots of the determinants. In addition we identify the standard Verma modules containing ‘no-label’ singular vectors (which are not detected directly by the roots of the determinants). We show that in standard Verma modules there are (at least) four different types of submodules, regarding size and shape. We also review the chiral determinant formula, for chiral Verma modules, adding new insights. Finally we transfer the results obtained to the Verma modules and singular vectors of the Ramond N = 2 algebra, which have been very poorly studied so far. This work clarifies several misconceptions and confusing claims appeared in the literature about the singular vectors, Verma modules and submodules of the topological N = 2 superconformal algebra. |
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