W-(infinity)-algebras in n complex dimensions and Kodaira-Spencer deformations : a symplectic approach

TL;DR

This paper extends the concept of W-infinity algebras from Riemann surfaces to n-dimensional complex manifolds using symplectic geometry, linking it to Kodaira-Spencer deformation theory and classical field theory.

Contribution

It introduces a symplectic framework for W-infinity algebras in higher complex dimensions and explores their relation to complex structure deformations.

Findings

W-infinity algebra extension to n complex dimensions

Connection with Kodaira-Spencer deformation theory

Classical field theoretical aspects discussed

Abstract

It is shown that the notion of W_\infty-algebra originally carried out over a (compact) Riemann surface can be extended to n complex dimensional (compact) manifolds within a symplectic geometrical setup. The relationships with the Kodaira-Spencer deformation theory of complex structures are discussed. Subsequently, some field theoretical aspects at the classical level are briefly underlined.