A Krichever--Novikov Formulation of W--Algebras on Riemann Surfaces

TL;DR

This paper extends the theory of classical W-algebras to higher genus Riemann surfaces using Krichever-Novikov methods, revealing connections with Lie algebra embeddings and complex geometry.

Contribution

It introduces a Krichever-Novikov formulation of W-algebras on Riemann surfaces, linking algebraic structures with geometric properties of complex curves.

Findings

Formulation of W-algebras on higher genus Riemann surfaces

Identification of relations between Lie algebra embeddings and surface geometry

New insights into the holomorphic structure of W-algebras

Abstract

It is shown how the theory of classical $W$--algebras can be formulated on a higher genus Riemann surface in the spirit of Krichever and Novikov. An intriguing relation between the theory of $A_1$ embeddings into simple Lie algebras and the holomorphic geometry of Riemann surfaces is exihibited.