ICTP Lectures on Covariant Quantization of the Superstring

TL;DR

This paper reviews the pure spinor approach to covariantly quantize the superstring, covering superparticle quantization, vertex operator construction, and curved background quantization with Ramond-Ramond flux.

Contribution

It provides a comprehensive review of the pure spinor formalism, including a new proof of superparticle equivalence and methods for superstring quantization in various backgrounds.

Findings

Established covariant quantization of the superparticle.

Constructed vertex operators for superstring amplitudes.

Extended quantization methods to curved backgrounds with flux.

Abstract

These ICTP Trieste lecture notes review the pure spinor approach to quantizing the superstring with manifest D=10 super-Poincare invariance. The first section discusses covariant quantization of the superparticle and gives a new proof of equivalence with the Brink-Schwarz superparticle. The second section discusses the superstring in a flat background and shows how to construct vertex operators and compute tree amplitudes in a manifestly super-Poincare covariant manner. And the third section discusses quantization of the superstring in curved backgrounds which can include Ramond-Ramond flux.