An Algorithm for Computing Four-Ramond Vertices at Arbitrary Level

TL;DR

This paper develops an explicit algorithm for computing four-Ramond vertices at any oscillator level, advancing the understanding of Ramond sector interactions in string theory.

Contribution

It introduces a novel sewing algorithm for Ramond vertices and derives a closed-form expression applicable at arbitrary oscillator levels.

Findings

Algorithm for four-Ramond vertex computation at any level

Closed-form expression for the four-vertex

Results for both complex and real fermions

Abstract

We perform the sewing of two (dual) Ramond reggeon vertices and derive an algorithm by means of which the so obtained four-Ramond reggeon vertex may be explicitly computed at arbitrary oscillator (mass) level. A closed form of the four-vertex is then deduced on the basis of a comparison to all terms obtained by sewing that contain only level zero and one oscillators. Results are presented for both complex fermions and for the previously studied case of real fermions.