The calculation of Feynman diagrams in the superstring perturbation theory

TL;DR

This paper introduces a new method for calculating multi-loop superstring amplitudes using Ward identities and superfield correlators on complex supermanifolds, addressing challenges in Ramond fermion loops.

Contribution

It proposes a novel approach to compute superstring amplitudes from gauge-independent Ward identities and constructs superconformal Schottky groups for all spinor structures.

Findings

Explicit formulas for amplitudes with even spinor structures

Method for correlators in Ramond fermion loops

Calculation of multi-loop boson emission amplitudes

Abstract

The method of the calculation of the multi-loop superstring amplitudes is proposed. The amplitudes are calculated from the equations that are none other than Ward identities. They are derived from the requirement that the discussed amplitudes are independent from a choice of gauge of both the vierbein and the gravitino field. The amplitudes are calculated in the terms of the superfields vacuum correlators on the complex (1|1) supermanifolds. The superconformal Schottky groups appropriate for this aim are built for all the spinor structures. The calculation of the multi- loop boson emission amplitudes in the closed, oriented Ramond-Neveu-Schwarz superstring theory is discussed in details. The main problem arises for those spinor structures that correspond to the Ramond fermion loops. Indeed, in this case the superfield vacuum correlators can not be derived by a simple extension of the boson string results. The method of the calculation of the above correlators is proposed. The discussed amplitudes due to all the even spinor structures is given in the explicit form.