I know sl(m|n) is the A-series Lie superalgebra by Kac
But in some literature, people also use the terminology su(m|n), which seems to be subclass of A-series. I am wondering how these two are related in general? For example, representeation theory or Lie algebra commutators?
Especially, people who study WZNW model on su(m|n) always start by discussing the sl(m|n) representations. I don't understand why. For example: https://arxiv.org/pdf/hep-th/0611147.pdf