The role of complex structures in w-symmetry

TL;DR

This paper explores how complex structures, especially those parametrized by Beltrami differentials, influence the formation of W-algebras within a symplectic framework, drawing parallels to conformal models.

Contribution

It introduces a novel perspective on the role of complex structures in W-symmetry, emphasizing the importance of Beltrami differentials in this context.

Findings

Complex structures parametrized by Beltrami differentials are crucial in W-algebra generation.

The symplectic approach parallels two-dimensional conformal models.

Beltrami differentials serve as fundamental elements in the construction of W-symmetries.

Abstract

In a symplectic framework, the infinitesimal action of symplectomorphisms together with suitable reparametrizations of the two dimensional complex base space generate some type of W-algebras. It turns out that complex structures parametrized by Beltrami differentials play an important role in this context. The construction parallels very closely two dimensional Lagrangian conformal models where Beltrami differentials are fundamental.