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

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.

13 pages. A remark about eq. $(1.8)$ has been added and a mistake in eq. $(4.6)$ has been corrected

References in corpus (3)

• W-symmetry in Conformal Field Theory
• The Covariant W_3 Action
• Finite and Infinite W Algebras and their Applications

Cited by in corpus (5)

• Primary currents and Riemannian geometry in W-algebras
• The Drinfeld--Sokolov Holomorphic Bundle and Classical $W$ Algebras on Riemann Surfaces
• Extrinsic Hermitian Geometry of Functional Determinants for Vector Subbundles and the Drinfeld--Sokolov Ghost System
• Drinfeld--Sokolov Gravity
• Toda Fields on Riemann Surfaces: remarks on the Miura transformation