Gluing of Branched Surfaces by Sewing of Fermionic String Vertices

TL;DR

This paper rigorously derives a closed-form expression for the four-fermion string vertex by sewing two Ramond two-fermion vertices, confirming previous results and treating all oscillator levels collectively.

Contribution

It provides a rigorous analytic derivation of the four-fermion string vertex in fermionic string theory, validating earlier partial results.

Findings

Closed-form expression for the four-fermion string vertex

Verification of previous partial results at all oscillator levels

Method treats all oscillator levels collectively

Abstract

We glue together two branched spheres by sewing of two Ramond (dual) two-fermion string vertices and present a rigorous analytic derivation of the closed expression for the four-fermion string vertex. This method treats all oscillator levels collectively and the obtained answer verifies that the closed form of the four vertex previously argued for on the basis of explicit results restricted to the first two oscillator levels is the correct one.