DDF and Pohlmeyer invariants of (super)string

TL;DR

This paper demonstrates how Pohlmeyer invariants of the bosonic string can be expressed via DDF invariants, enabling consistent quantization and generalization to superstrings and various backgrounds.

Contribution

It establishes a link between Pohlmeyer and DDF invariants and extends their applicability to superstrings and diverse backgrounds with free field realizations.

Findings

Expressed Pohlmeyer invariants in terms of DDF invariants

Quantization yields a consistent algebra of invariants

Generalized invariants to superstrings and backgrounds

Abstract

We show how the Pohlmeyer invariants of the bosonic string are expressible in terms of DDF invariants. Quantization of the DDF observables in the usual way yields a consistent quantization of the algebra of Pohlmeyer invariants. Furthermore it becomes straightforward to generalize the Pohlmeyer invariants to the superstring as well as to all backgrounds which allow a free field realization of the worldsheet theory.