Factorization of bosonic string amplitudes |
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| Institution: | 1. Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany;2. Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany;3. Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, UK;4. Maxwell Institute for Mathematical Sciences, Edinburgh, UK;5. The Higgs Centre for Theoretical Physics, Edinburgh, UK;1. Department of Physics, KU Leuven Campus Kortrijk - KULAK, Etienne Sabbelaan 53, 8500 Kortrijk, Belgium;2. Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, 9000 Gent, Belgium;3. Departamento de Física Teórica, Instituto de Física, UERJ - Universidade do Estado do Rio de Janeiro, Brazil;4. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany |
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| Abstract: | We consider the bosonic string path integral over degenerating Riemann surfaces. We first review the factorization of conformal field theory on a degenerating surface. A careful treatment of the degeneration of the measure for moduli leads to a modification of the usual ghost insertions so as to assure covariance under a change of conformal frame. More generally, amplitudes with BRST invariant but conformally non-invariant operators are well defined with the covariant ghost insertions. As a detailed application we study the string modifications to the background field equations. We find to first order in the tadpole and all orders in string coupling that the ratio of the graviton source, dilaton source, and zero-point amplitude agrees with that found from general covariance and the soft-dilaton theorem in the low-energy field theory. We also discuss the unitarity of the bosonic string theory, |
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