Topological field theories,Nicolai maps and BRST quantization |
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| Institution: | 1. Laboratory for Provenance Studies, Department of Earth and Environmental Sciences, University of Milano-Bicocca, Milano, Italy;2. Geology Department, Cairo University, Giza, Egypt;1. Servicio de Aparato Digestivo, Hospital Clínico Universitario Lozano Blesa, Zaragoza, España;2. Instituto de Investigación Sanitaria (ISS) Aragón, Zaragoza, España;3. Departamento de Medicina, Facultad de Medicina, Universidad de Zaragoza, Zaragoza, España;1. Université de Paris, Institut de Physique du Globe de Paris, 75005 Paris, France;2. Institut Universitaire de France, France;1. Second Clinic of Orthopaedics and Kinetic Organ Traumatology, Medical University of Gdansk, Gdansk, Poland;2. Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Gdansk, Poland;3. Department of Neurosurgery, Medical University of Gdansk, Gdansk, Poland;1. Institut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr. 12, D-89081 Ulm, Germany;2. Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany;3. Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia;1. Department of Oral and Maxillofacial Surgery, Peking University School and Hospital of Stomatology, Beijing 100081, China;2. National Clinical Research Center for Oral Diseases, Beijing 100081, China |
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| Abstract: | We establish a connection between topological field theories, Nicolai maps, BRST quantization and Langevin equations. In particular we show that there is a one-to-one correspondence between global unbroken supersymmetric theories which admit a Nicolai map and theories which arise as the BRST quantization of the square of the Langevin equation, setting the random field to zero. As such they are topological in nature. As an example we consider the topological quantum field theory of Witten in the Labastida-Pernici form and show that it is the first example of a theory admitting a complete Nicolai map in four dimensions. We also consider the topological sigma models of Witten and show that they too arise from the BRST quantization of the square of the Langevin equation. |
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