Aspects of the affine superalgebra sl(2-vertical bar-1) at fractional level

In this thesis we study the affine superalgebra s-tilde-l(2-vertical bar-1; C) at fractional levels of the form k = 1/u - 1, u is an element of N-back slash {1}. It is for these levels that admissible representations exist, which transform into each other under modular transformations. In the second chapter we review background material on conformal field theory, particularly the Wess-Zumino-Witten model and the connection with modular transformations. The superalgebra sl(2-vertical bar-1; C) is introduced, as is its affine version. The next chapter studies the modular transformation properties of s-tilde-l(2-vertical bar-1; C) characters. We derive formulae for these transformations for all levels of the form k = 1/u - 1, u is an element of N-back slash {1}. We also investigate some modular invariant combinations of characters and find two series of modular invariants, analogous to the A- and D-series of the classification of s-tilde-l(2) modular invariants. In chapter 4 we turn to the study of fusion rules. We concentrate on the case k = -1/2. By considering the decoupling of singular vectors, we are able to find consistent fusion rules for this particular level. These fusion rules correspond to a modular invariant found in chapter 3. This study suggests that one may consistently define a conformal field theory based on s-tilde-l(2-vertical bar-1; C) at fractional level. (author)