On the Normalization and Hermiticity of Amplitudes in 4D Heterotic Superstrings

TL;DR

This paper addresses the normalization of scattering amplitudes in 4D heterotic superstrings, ensuring unitarity and hermiticity, and provides explicit formulas for vertex operator transformations.

Contribution

It introduces a consistent normalization scheme for amplitudes and vertex operators in 4D heterotic superstrings, linking hermiticity to amplitude properties.

Findings

Normalized vacuum and vertex operators at each genus

Explicit map relating incoming and outgoing vertex operators

Ensured unitarity and hermiticity of scattering amplitudes

Abstract

We consider how to normalize the scattering amplitudes of 4D heterotic superstrings in a Minkowski background. We fix the normalization of the vacuum amplitude (the string partition function) at each genus, and of every vertex operator describing a physical external string state in a way consistent with unitarity of the $S$-matrix. We also provide an explicit expression for the map relating the vertex operator of an incoming physical state to the vertex operator describing the same physical state, but outgoing. This map is related to hermitean conjugation and to the hermiticity properties of the scattering amplitudes.