Multiloop World-Line Green Functions from String Theory

Abstract

We show how the multiloop bosonic Green function of closed string theory reduces to the world-line Green function as defined by Schmidt and Schubert in the limit where the string world-sheet degenerates into a ${\Phi }^3$ particle diagram. To obtain this correspondence we have to make an appropriate choice of the local coordinates defined on the degenerate string world sheet. We also present a set of simple rules that specify, in the explicit setting of the Schottky parametrization, which is the corner of moduli space corresponding to a given multiloop ${\Phi }^3$ diagram.

33 pages, 6 figures. Published version

References in corpus (9)

• Calculation of Graviton Scattering Amplitudes using String-Based Methods
• Worldline Green Functions for Multiloop Diagrams
• Multiloop Calculations in the String-Inspired Formalism: The Single Spinor-Loop in QED
• Propagators and Path Integrals
• Axial Couplings on the World-Line
• Yukawa Couplings for the Spinning Particle and the World Line Formalism
• Bern-Kosower Rule for Scalar QED
• Relation between Worldline Green Functions for Scalar Two-Loop Diagrams
• Relations between some analytic representations of one-loop scalar integrals

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