Calculation of Feynman diagrams in superstring perturbation theory.

Abstract

A method of perturbative calculation of multiloop amplitudes in superstring theories is proposed. In this method the multiloop superstring amplitudes are calculated from equations that are none other than Ward identities. These equations are derived from the requirement that the discussed amplitudes are independent of the choice of gauge of both the [ital vierbein] and the gravitino field. The amplitudes in question are determined in a unique way by these equations together with the factorization condition on the multiloop amplitudes when two handles move away from each other. The considered amplitudes are calculated in terms of vacuum correlators of superfields defined on the complex (1[vert bar]1) supermanifolds. These supermanifolds are described by superconformal versions of Schottky groups. The superconformal Schottky groups appropriate for this aim are built for all spinor structures. Being based only on gauge invariance together with the factorization requirement on the multiloop amplitudes when the handles move away from each other (unitarity), the proposed method can be used widely in critical (super)string theories. Moreover, after an appropriate modification is made, this method can be employed for the noncritical (super)string, too. In this paper the closed, oriented Ramond-Neveu-Schwarz superstring is considered, only boson emission amplitudes being discussed. The more » problem of the calculation of the multiloop boson emission amplitudes is concentrated mainly on those spinor structures where superfields are branched on the complex [ital z] plane where Riemann surfaces are mapped. In this case the vacuum superfield correlators cannot be derived by a simple extension of the boson string results. The method of calculation of the above correlators is proposed. The multiloop amplitudes associated with all the even spinor structures are calculated in explicit form. A previous discussion of the divergence problem is given. « less