BRST Quantisation of the N=2 String in a Real Spacetime Structure

TL;DR

This paper investigates the BRST quantization of the N=2 string in a real (2,2) spacetime, revealing new features in operator relations, picture-changing operators, and the physical spectrum, with implications for string interactions.

Contribution

It introduces a novel analysis of the N=2 string with real spacetime structure, highlighting the non-invertibility of picture-changing operators and the resulting distinct physical spectra.

Findings

Operator $ ext{exp}( ext{lambda} ext{int} J^{ ext{tot}})$ is local in the diagonal basis.

Picture-changing operators are non-invertible in the diagonal basis.

Physical operators in different pictures cannot be identified due to non-invertible picture-changing operators.

Abstract

We study the $N=2$ string with a real structure on the $(2,2)$ spacetime, using BRST methods. Several new features emerge. In the diagonal basis, the operator $\exp(\lambda \int^z J^{\rm tot})$, which is associated with the moduli for the $U(1)$ gauge field on the world-sheet, is local and it relates the physical operators in the NS and R sectors. However, the picture-changing operators are non-invertible in this case, and physical operators in different pictures cannot be identified. The three-point interactions of all physical operators leads to three different types of amplitudes, which can be effectively described by the interactions of a scalar NS operator and a bosonic spinorial R operator. In the off-diagonal bases for the fermionic currents, the picture-changing operators are invertible, and hence physical operators in different pictures can be identified. However, now there is no local operator $\exp(\lambda \int^z J^{\rm tot})$ that relates the physical operators in different sectors. The physical spectrum is thus described by one scalar NS operator and one spinorial R operator. The NS and R operators give rise to different types of three-point amplitudes, and thus cannot be identified.