Admissible representations and characters of the affine superalgebras osp(l,2) and ŝl(2|l)

Abstract

In this thesis we compute characters and supercharacters of irreducible admissible representations for the two affine superalgebras osp(l,2;C) and l(2|l;C).The work on osp(l, 2; C) includes a derivation of the embedding diagram. We compute the modular transformations of the Neveu-Schwarz characters of osp(l, 2; C) and show that they transform in a manner consistent with the different possible free fermion spin structures on a torus. In chapter 3 we turn our attention to ŝl(2|l;C). Characters and supercharacters are computed for three classes of admissible representation. We have to derive the embedding diagram for one of these classes. We show that the integrable characters in the classes we study are identical to characters of the N = 4 superconformal algebra and that some of the sl(2|l;C) characters have a pole in a certain limit. The residue at this pole is computed and it is found to be proportional to an N = 2 minimal character. Specialising to fractional levels k of the form k + 1 = l/u,u ϵ N, we consider the SL(2|1)/SL{2) coset theory and make a conjecture that it is a product of a parafermion theory and a rational torus model. The appearance of parafermion characters and rational torus model characters in the branching functions of some examples that we have worked out leads to a conjecture for the general form of the branching functions whenever the level k has the form k + 1 = 1/u.The modular T transformation can be worked out easily for any character or super- character we have computed. We work out the 5 transformation of the Neveu-Schwarz characters in two examples and find that we get a unitary S-matrix in each case. The thesis finishes with some interesting identities between ŝu(2) string functions which are a corollary of the work on branching functions. [brace not closed]