Conformal Field Theory and Vertex Operator Algebras

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Description

Time: Mondays, 11.00-13.00

Location for Maxwell Institute students: Bayes Centre (room 5.46)

Module Leader: Anatoly Konechny (Heriot-Watt University)

Module Summary

This course is intended to provide both the introduction to two-dimensional conformal field theory (2D CFT) and 

to give an opportunity to learn more advanced topics linked to current research. 2D CFT is a well-developed branch of mathematical physics with many connections to other  topics in mathematics such as infinite-dimensional Lie algebras, vertex operator algebras, modular tensor categories and theory of modular forms. 

The course starts with lectures covering the basics  such as  conformal geometry on the (extended) complex plain, correlation functions, Ward identities, radial quantisation, operator product expansion, Virasoro algebra and conformal families. This part is planned to be covered in 5-6 lecturers to be followed by 2 lectures focussed on Vertex Operator Algebras. The students are then offered a number of guided reading projects on more advanced topics such as conformal blocks, WZW theories, AGT conjecture and more. Brief informal presentations on their reading topics are expected to be given by the students in the last 2 lectures.

The course does not assume any prior knowledge of quantum field theory and may serve as an introduction into this topic for mathematicians. The main prerequisite for the course is basic knowledge of quantum mechanics although the essential concepts will be reminded along the way. Some basic knowledge of groups, differential geometry, functional and complex analysis is also assumed. A detailed set of notes covering the introductory part along with 9 fully worked tutorial sheets for self practice will be provided.

Assessment: based on brief presentations on the chosen reading topics, in the last two weeks