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Covariant string amplitudes on exotic topologies to one loop
Institution:1. Physics Department, Indiana University, Bloomington, IN 47405, USA;2. Theoretical Division, CERN, 1211 Genève 23, Switzerland;3. City College of New York, 138th and Convent Ave., New York, NY 10031, USA;1. Institut für Physik, Humboldt-Universität zu Berlin, D–10099 Berlin, Germany;2. Theoretical Physics Department, CERN, Geneva, Switzerland;3. Max-Planck-Institut für Physik, Föhringer Ring 6, D–80805 Munich, Germany;4. Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA;5. CP3, Université Catholique de Louvain, B–1348 Louvain-la-Neuve, Belgium;6. All Souls College, University of Oxford, OX1 4AL, Oxford, UK
Abstract:Rules are provided for the calculation of string amplitudes on all exotic topologies to one loop. These topologies include the real projective plane, the disk, the annulus, the Möbius strip, the torus and the Klein bottle. The rules are valid for bosonic strings, superstrings, and heterotic strings either in their critical dimensions or toroidally compactified, and they are applicable to amplitudes with arbitrary external bosonic and fermionic states, including mixed open- and closed-string transitions. The modular invariance of the torus amplitudes is discussed.
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