# Orbifold actions and twist operators

+ 3 like - 0 dislike
63 views

A twist operator $\sigma$ is the operator that acts on the untwisted vacuum $|0\rangle$ to create a twisted vacuum $\sigma|0\rangle$. States belonging to the twisted sector of an orbifold are built on such twisted vacua (which are also in 1-1 correspondence with the fixed points of the orbifold action).

My question is given a specific twist operator $\sigma$, how can I possibly deduce the orbifold action that corresponds to it?

More specifically, let
$$\sigma=\psi^1+i\psi^2$$
the operator that arises after bosonizing two real fermions. If the boundary conditions for the fermions are known, let's say $\psi^1\rightarrow \psi^1$ and $\psi^2\rightarrow -\psi^2$ then we have some information on $\sigma$. We should be able to interpret this $\sigma$ as the twist operator that generates a twisted sector of some orbifold, but what would the orbifold action in this case be?

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverfl$\varnothing$wThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.