Using of unitarity equations for the calculation of fermion interaction amplitudes in the superstring theory

TL;DR

This paper applies unitarity equations to compute fermion interaction amplitudes in superstring theory, explicitly deriving a 4-point amplitude involving Ramond states and verifying related integral relations.

Contribution

It introduces a method using unitarity equations to calculate fermion interaction amplitudes including Ramond states in superstring theory.

Findings

Explicit 4-point amplitude with two Neveu-Schwarz and two Ramond states derived.

Integral relations for local functions in amplitude calculations verified at tree level.

Method extends unitarity-based calculations to fermionic sectors in superstring theory.

Abstract

The unitarity equations for the boson interaction amplitudes in the superstring theory are used to calculate the interaction amplitudes including the Ramond states, which are 10-fermion and Ramond bosons. The n-loop, 4-point amplitude with two massless Neveu-Schwarz bosons and two massless Ramond states is obtained explicitly. It is shown that, in addition, the unitarity equations require some integral relations for local functions determining the amplitude. For the tree amplitude the validness of the above integral relations is verified.