AG Mathematische Physik, Thomas Creutzig (FAU): Towards logarithmic conformal field theory

Thomas Creutzig (FAU)

Towards logarithmic conformal field theory

Abstract:

A vertex operator algebra is the algebraic notion of chiral (and

anti-chiral) algebra in two-dimensional conformal field theory. VOAs are

an established subject of mathematics in its own right, but connecting

to the physics of two-dimensional CFT is still difficult. This

difficulty arises as VOA is of algebraic nature while the observables in

CFT, the correlation functions, are of analytic nature.

Representation theory of modern VOAs almost exclusively is non

semi-simple, which should lead to logarithmic CFT, that is CFTs whose

correlation functions can have logarithms.

I will define full logarithmic VOAs, which have exactly the features

that one wants a genus zero logarithmic CFT to have, and will give an

example.