Worldsheet complex structure

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