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

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