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Glimpses of Logarithmic Conformal Field Theory

M. Flohr (Hannover)

26.06.2008 at 16:15 

We give a brief survey on logarithmic conformal field theory (LCFT). The characterizing feature of LCFT is the occurrence of indecomposable representations of the chiral symmetry algebra.  We point out that LCFT is a rather general kind of conformal field theory  with many applications, and not just a set of a few pathological cases.  We then review how most  of the powerful structures of rational conformal  field theory can be generalized to the logarithmic case. In fact, it can be proven that certain LCFTs are rational in the mathematically strong sense. We present two further recent results: Firstly, fermionic sum representations of the characters of certain LCFTs show that these theories naturally fit into the classification scheme of rational CFTs via their modular properties. Secondly, the construction of augmented minimal models suggests that any rational CFT may be extended to a (rational) LCFT.

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