Three particle superstring amplitudes with massive legs

TL;DR

This paper develops solutions to Ward identities for three-particle superstring scattering amplitudes with massive legs, providing explicit formulas and exploring their applications in string theory in various dimensions.

Contribution

It presents the general solutions of Ward identities for three-particle amplitudes with massive legs in supersymmetric theories, including explicit results for superstring amplitudes in ten and eight dimensions.

Findings

Explicit three-point amplitudes with one massive leg derived

Solutions dictated entirely by super-Poincare symmetry

Extension to higher point amplitudes initiated

Abstract

On-shell superspaces and associated spinor helicity techniques give an efficient formulation of the Ward identities of on-shell supersymmetry for scattering amplitudes and supply tools to construct their solutions. Based on these techniques in this paper the general solutions of the Ward identities are presented for three particle scattering amplitudes with one, two or three massive legs for simple supersymmetry in ten and eight dimensions. It is shown in examples how these solutions may be used to obtain concrete amplitudes for the closed (IIB) and open superstring in a flat background. Explicit results include all three point amplitudes with one massive leg whose functional form is shown to be dictated completely by super-Poincare symmetry. The resulting surprisingly simple series only involves massive superfields labelled by completely symmetric little group representations. The extension to more general explicit three and higher point amplitudes in string theory is initiated. In appendices the field content of the fundamental massive superfields of the open and closed superstring are listed in terms of the Dynkin labels of a variety of groups which may be of independent interest.