I am trying to understand the vertex operator algebras of the following form:


Where $U(M|N)$ is the unitary supergroup, $U(L)$ is the usual unitary group, and $k_1$ and $k_2$ are the levels, respectively. I want to know the followings:

  • For a specific embedding of $U(L)$ inside $U(M|N)$, how can I determine the highest-weight states of $\frac{U(M|N)_{k_1}}{U(L)_{k_2}}$? More specifically, how can I label these highest-weight states?

  • What is the conformal dimension (the eigenvalue of the $\widehat{L}_0$ operator) of these highest-weight states?

  • What happens if $M=L$ and the embedding is the trivial embedding of $U(M)$ inside $U(M|N)$?

  • How can I characterize the highest-weight states in the general case, namely $\frac{G_{k_1}}{H_{k_2}}$, where $H$ is a subgroup of $G$?

A reference is highly appreciated.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.