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Logarithmic vertex operator algebras (introductory lecture)

Banff International Research Station for Mathematical Innovation and Discovery

In this introductory lecture I would like to discuss vertex operator algebras which allow for non-semisimple representations. There will be two parts, which will roughly relate to genus 0 and genus 1 properties. In the first part I will try to motivate why one might want to look at such VOAs and give the basic example, symplectic fermions. We will briefly look at VOA modules and intertwiners to get an idea of how the category of VOA modules can become a braided monoidal category. For the second part we look at certain traces over VOA modules and modular properties of conformal blocks on the torus. These have an intriguing relation to tensor product multiplicities, known as the Verlinde formula, which is a theorem for finitely semisimple theories and a conjecture without the semisimplicity assumption.

Mathematics; Algebraic geometry; Quantum theory; Mathematical physics

video/mp4

Author affiliation: U Hamburg

2019-03-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69270

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/