Скачать или смотреть CFT, Thomas Creutzig, VOA lectures

Thomas Creutzig

FAU Erlangen

Title: Fractional level WZW theories of sl(2)
Abstract: Logarithmic CFT at present has been mainly studied in examples and a key example isthe fractional level WZW theory of sl(2), that is in VOA language the study of the category of weight modules of the affine vertex algebra of sl(2). By now this category is understood in the sense that one has a full classification of modules, one knows that the category is a ribbon
category and fusion rules are also known. All these results required new insights and I plan to give an introductory overview over these works as follows:
1) A discussion of weight modules of the finite dimensional Lie algebra sl(2) as a warm-up
2) Lifting this discussion to the affine Lie and vertex algebras and stating the classification result of weight modules
3) The Virasoro algebra is well-known to be the Drinfeld-Sokolov reduction of the affine vertex algebra of sl(2). This can be somehow inverted and this will be used for a novel construction of logarithmic modules
4) The Kazama-Suzuki duality of string theory is in particular a correspondence between the WZW theory of sl(2) and the N=2 super conformal algebra. This correspondence can be used to get a braided tensor category structure.
5) If time permits I can cover rigidity, fusion rules, Verlinde’s formula and a correspondence to the quantum supergroup of sl(2|1).

Université Paris-Saclay Institut Pascal

01/10/2025