Covariant Quantization of the Superstring

TL;DR

This paper presents a covariant quantization method for the superstring using pure spinor ghosts, enabling computation of N-point amplitudes in a ten-dimensional super-Poincaré covariant framework, and extends to curved backgrounds.

Contribution

It introduces a covariant quantization approach for the superstring with pure spinor ghosts, allowing for explicit amplitude calculations and background generalizations.

Findings

Constructed a BRST operator from fermionic constraints.

Computed N-point tree amplitudes covariantly.

Extended quantization to curved supergravity backgrounds.

Abstract

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators are constructed and, for the first time, N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincar\'e covariant manner. Quantization can be generalized to curved supergravity backgrounds and the vertex operator for fluctuations around $AdS_5\times S^5$ is explicitly constructed. This review is written in a self-contained manner and is based on talks given at the Fradkin Memorial Conference and Strings 2000.