Correlation functions from two-dimensional string Ward identities

TL;DR

This paper derives and solves correlation function recursion relations from two-dimensional string Ward identities, clarifying their connection to charge conservation and extending the framework to open strings.

Contribution

It provides a novel derivation of $w_ abla$ Ward identities using canceled propagators and explicitly computes certain correlation functions, extending the understanding of string symmetries.

Findings

Derived $w_ abla$ Ward identities from gauge invariances

Calculated correlation functions exactly

Extended Ward identities to open strings

Abstract

We rederive the $w_\infty$ Ward identities, starting from the existence of trivial linearized gauge invariances, and using the method of canceled propagators in the operator formalism. Recursion relations for certain classes of correlation functions are derived, and these correlation function are calculated exactly. We clarify the relation of these results with another derivation of the Ward identities, which relies directly on charge conservation. We also emphasize the importance of the kinematics of canceled propagators in ensuring that the Ward identities are non-trivial. Finally, we sketch an extension of Ward identities to open strings.