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arXiv · 1511.01659

Calculation of multi-loop superstring amplitudes

G. S. Danilov
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Abstract

Multi-loop interaction amplitudes in the theory of the closed, oriented superstrings are obtained by the integration of local amplitudes which are represented by a sum of the spinning string local amplitudes. The last local amplitudes are given explicitly through super-Schottky group parameters and interaction vertex coordinates on the $(1|1)$ complex supermanifold. The integration is ambiguous under those replacements of the integration variables which admix Grassmann variables to the boson ones. So the calculation is guided by a preservation of local symmetries of the superstring. The obtained amplitudes are free from divergences and consistent with the world-sheet symmetries. The vacuum amplitude and 1-, 2- and 3-point amplitudes of massless states vanish once the integration over certin modular variables and interaction vertex coordinates.

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G. S. Danilov. 2015-11-05. Calculation of multi-loop superstring amplitudes. https://doi.org/10.1088/0264-9381%2F33%2F23%2F235012

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