Worldsheet complex structure

Eigenvectors of on :

On functions only:

We will sometimes write and instead of and .

Such notations may be useful because they provide a natural shortcut ,

For a one-form , we will introduce the following notations. Let denote the following one-form:

The definition of is completely analogous.

This is a natural notation; for and , the combination can only mean one thing

In physics literature it it common to write instead of ; this is the projector on the left-moving component

index  introduction  notations  supergeometry  BV-formalism  BRST-formalism  equivariant-cohomology  bosonic-string  omega  omega-BRST  contact-structure  transfer  tangent-space-of-double-coset  integrated-vertex  unintegrated-vertex  boundary  picture-changing  Heterotic-RNS  Type-II-RNS  N2Superconformal  twisting  pure-spinor  left-sector  open-problems