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Durham e-Theses
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Modular transformations of admissible N = 2 and Affine sl(2|1;C) characters

Sadeghi, Jafar (2002) Modular transformations of admissible N = 2 and Affine sl(2|1;C) characters. Doctoral thesis, Durham University.



This thesis is a study of the affine super-algebra sl(2|l; C) and N = 2 superconformal algebra at fractional levels. In the first chapter we review background material on Conformal Field Theory, and how it appears in the context of string theory and the Wess - Zumino – Novikov - Witten model. We also discuss integrable and admissible representations of infinite dimensional algebras and their modular transformations. In Chapter 2 we elaborate some more on modular transformations and we derive them in the case of non - unitary minimal N = 2 characters. Some very explicit formulas are presented. In Chapter 3 we discuss character formulas for the affine sl(2|l;C) algebra and some of their general properties are given, in particular their behaviour under spectral flow. In Chapter 4 we turn to the study of sumrules for sl(2|l;C) at level k. These involve the product of sl(2) characters at level k, k', and 1 with {k + l){k' + !) = 1. We consider k + 1 = for = 1, p e Z*, u eN and show that the sumruleswe have obtained agree with the literature when the parameter p is restricted to p = 1. We use the integral form of the sumrules to study the modular properties of sl(2|l) characters at fractional level in the last section of Chapter 4.The advisor for this work has been Dr. Anne Taormina. [brace not closed]

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Thesis Date:2002
Copyright:Copyright of this thesis is held by the author
Deposited On:26 Jun 2012 15:22

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