Aspects of the Affine Superalgebra sl(2|l) at Fractional Level Ph.D. Thesis by Gavin Balfour Johnstone, April 2001 In this thesis we study the affine superalgebra sl(2|l; C) at fractional levels of the form k = l/u-l,uєN\{l}. 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|l;C) is introduced, as is its affine version. The next chapter studies the modular transformation properties of sl(2|l;C) characters. We derive formulae for these transformations for all levels of the form K = 1/u-1,uєN\{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 sl{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 sl(2|l;C) at fractional level.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:342615 |
| Date | January 2001 |
| Creators | Johnstone, Gavin Balfour |
| Publisher | Durham University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.dur.ac.uk/3956/ |
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