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?


1 Answer 1


For a toroidal orbifold, suppose you know the boundary condition in the k-twisted sector and the spin structure $\alpha, \beta \in \lbrace 0,1/2\rbrace $. In light cone gauge you have:

$\psi^{j}(\sigma^0, \sigma^1+2\pi)=- e^{2\pi i \alpha }e^{2\pi i k v_j }\psi^{j}(\sigma^0, \sigma^1)$



in which $a_j$ are some integer, fixed by the possible crystallographic actions. From this boundary condition you can get N of the $Z_N$ orbifold.

Check "Basics concepts of String Theory", (Lust, Theisen, Bluemenhagen), pag.306


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.