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Calculation of multi-loop superstring amplitudes. (English) Zbl 1354.83053

Summary: The multi-loop interaction amplitudes in the closed, oriented superstring theory are obtained by the integration of local amplitudes. The local amplitude is represented by a sum over the spinning string local amplitudes. The spinning string local amplitudes are given explicitly through super-Schottky group parameters and through interaction vertex coordinates on the \((1\mid1)\) complex, non-split supermanifold. The obtained amplitudes are free from divergences. They are consistent with the world-sheet spinning string symmetries. The vacuum amplitude vanishes along with 1-, 2- and 3-point amplitudes of massless states. The vanishing of the above-mentioned amplitude occurs after the integration of the corresponding local amplitude has been performed over the super-Schottky group limiting points and over interaction vertex coordinate, except for those \((3\mid2)\) variables which are fixed due to \(\mathrm{SL}(2)\)-symmetry.

MSC:

83E30 String and superstring theories in gravitational theory
81T20 Quantum field theory on curved space or space-time backgrounds
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