An Introduction to the Covariant Quantization of Superstrings

TL;DR

This paper introduces a new covariant quantization method for superstrings that avoids pure spinor constraints, building on and comparing with existing approaches like Green-Schwarz and Berkovits.

Contribution

It presents a novel covariant superstring quantization framework without pure spinor constraints, linking grading and homological perturbation theory.

Findings

Provides a self-contained formulation of the covariant quantization method.

Clarifies the relation between grading and homological perturbation theory.

Compares the new approach with existing superstring quantization methods.

Abstract

We give an introduction to a new approach to the covariant quantization of superstrings. After a brief review of the classical Green--Schwarz superstring and Berkovits' approach to its quantization based on pure spinors, we discuss our covariant formulation without pure spinor constraints. We discuss the relation between the concept of grading, which we introduced to define vertex operators, and homological perturbation theory, and we compare our work with recent work by others. In the appendices, we include some background material for the Green-Schwarz and Berkovits formulations, in order that this presentation be self contained.