Off-shell Supersymmetry versus Hermiticity in the Superstring

TL;DR

This paper explores the unusual hermiticity properties of the N=1 RNS superstring caused by off-shell supersymmetry and shows these properties are natural within an N=2 superstring framework.

Contribution

It reveals the connection between off-shell supersymmetry in N=1 superstrings and hermiticity properties, clarified through embedding into N=2 superstrings.

Findings

Off-shell N=1 supersymmetry implies unusual hermiticity properties.

Embedding N=1 into N=2 superstring makes hermiticity properties natural.

Highlights the structural differences between N=1 and N=2 superstrings.

Abstract

We point out that off-shell four-dimensional supersymmetry implies strange hermiticity properties for the N=1 RNS superstring. However, these hermiticity properties become natural when the N=1 superstring is embedded into an N=2 superstring.