Spectrum generating algebra for the pure spinor superstring

TL;DR

This paper develops a DDF-like algebraic framework within the pure spinor formalism to systematically construct physical vertex operators at all mass levels using $SO(8)$ superfields.

Contribution

It introduces a novel algebraic construction that simplifies the derivation of vertex operators in the pure spinor superstring formalism.

Findings

Derived creation/annihilation algebra from light-cone vertices

Systematic construction of vertex operators at any mass level

Unified integrated and unintegrated vertex operator forms

Abstract

In this work, a DDF-like construction within the pure spinor formalism is presented. Starting with the light-cone massless vertices, the creation/annihilation algebra is derived in a simple manner, enabling a systematic construction of the physical vertex operators at any mass level in terms of $SO\left(8\right)$ superfields, in both integrated and unintegrated forms.