Primary currents and Riemannian geometry in W-algebras

TL;DR

This paper demonstrates that primary currents in finite chiral W-algebras can be described using pure gravitational variables, based on consistency requirements related to complex analytic changes of charts.

Contribution

It establishes a connection between primary currents in W-algebras and gravitational variables through geometric consistency conditions.

Findings

Primary currents are described in terms of gravitational variables.

Consistency under complex analytic changes constrains the structure of W-algebras.

The approach links algebraic structures to geometric and gravitational concepts.

Abstract

It is proved that general consistency requirements of stability under complex analytic change of charts show that primary currents in finite chiral W-algebras are described in terms of pure gravitational variables.