On the complete classification of unitary N=2 minimal superconformal field theories [Elektronische Ressource] / Oliver Gray

On the complete classi cation of unitary N = 2minimal superconformal eld theoriesOliver GrayDoctoral Thesissubmitted to theFaculty of Mathematics and Natural Sciencesof the University of AugsburgSeptember 2009First referee: Prof. Dr. Katrin WendlandSecond Prof. Dr. Terry GannonDate of oral examination: 3rd August 2009AbstractAiming at a complete classi cation of unitary N = 2 minimal models (wherethe assumption of space-time supersymmetry has been dropped), it is shownthat each candidate for a modular invariant partition function of such a the-ory is indeed the partition function of a minimal model. A family of modelsconstructed via orbifoldings of either the diagonal model or of the space-timesupersymmetric exceptional models demonstrates that there exists a unitaryN = 2 minimal model for every one of the allowed partition functions in the listobtained from Gannon’s work [26].Kreuzer and Schellekens’ conjecture that all simple current invariants canbe obtained as orbifolds of the diagonal model, even when the extra assumptionof higher-genus modular invariance is dropped, is con rmed in the case of theunitary N = 2 minimal models by simple counting arguments.We nd a nice characterisation of the projection from the Hilbert space of aminimal model with k odd to its modular invariant subspace, and we present anew simple proof of the superconformal version of the Verlinde formula for theminimal models using simple currents.