Loop models for CFTs

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Abstract

By interpreting the fusion matrix as an adjacency matrix we associate a loop model to every primary operator of a generic conformal field theory. The weight of these loop models is given by the quantum dimension of the corresponding primary operator. Using the known results for the O(n) models we establish a relationship between these models and SLEs. The method is applied to WZW, \(c<1\) minimal conformal field theories and other coset models.

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Exact Critical Point and Critical Exponents ofO(n)Models in Two Dimensions

Bernard Nienhuis (1982)

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Bits and Pieces in Logarithmic Conformal Field Theory

Michael Flohr (2001)

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.