Covariant Quantization of the Green-Schwarz Superstring in a Calabi-Yau Background

TL;DR

This paper presents a covariant quantization method for the four-dimensional Green-Schwarz superstring in a Calabi-Yau background, enabling calculations of superstring amplitudes with manifest symmetries.

Contribution

It introduces a new covariant quantization approach incorporating an N=2 superconformal algebra and constructs BRST-invariant vertex operators for superstring amplitude computations.

Findings

First-class constraints form an N=2 superconformal algebra with c=-3

Combined system forms a critical N=2 string with c=6

Superstring amplitudes can be computed on N=2 super-Riemann surfaces

Abstract

After adding a scalar chiral boson to the usual superspace variables, the four-dimensional Green-Schwarz superstring is quantized in a manifestly SO(3,1) super-Poincar\'e covariant manner. The constraints are all first-class and form an N=2 superconformal algebra with $c=-3$. Since the Calabi-Yau degrees of freedom are described by an N=2 superconformal field theory with $c=9$, the combined Green-Schwarz and Calabi-Yau systems form the $c=6$ matter sector of a critical N=2 string. Using the standard N=2 super-Virasoro ghosts, a nilpotent BRST charge is defined and vertex operators for the massless supermultiplets are constructed. Four-dimensional superstring amplitudes can be calculated with manifest SO(3,1) super-Poincar\'e invariance by evaluating correlation functions of these BRST-invariant vertex operators on N=2 super-Riemann surfaces.