Bits and Pieces in Logarithmic Conformal Field Theory

Details Bits and Pieces in Logarithmic Conformal Field Theory Bits and Pieces in Logarithmic Conformal Field Theory

2001-11-25

arxiv.org/abs/hep-th/0111228v2

Int.J.Mod.Phys.A18:4497-4592,2003

Physics

High Energy Physics

High Energy Physics - Theory

91 pages, notes of lectures delivered at the first School and Workshop on Logarithmic Conformal Field Theory and its Applicati

Scientific paper

10.1142/S0217751X03016859

These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. These two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.

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