Correlators in conformal field theory - a case for category theory
Organizers
Speaker
Jürgen Fuchs
Time
Wednesday, September 17, 2025 5:00 PM - 6:30 PM
Venue
A6-101
Online
Zoom 388 528 9728
(BIMSA)
Abstract
The quantum field theoretic notion of a correlator, or correlation function, can be made mathematically precise for CFTs, i.e. for two-dimensional conformal quantum field theories. For these, a correlator can be characterized as a specific element in a certain vector space, the space of conformal blocks, that is obtained from the conformal (and further) symmetries of the CFT. I will describe several methods that allow one, for wide classes of models, to construct all correlators of a CFT as elements in conformal block spaces, in such a way that all (infinitely many) consistency conditions are fulfilled. I will also explain how algebraic structures in tensor categories and higher categories enter these constructions. But no prior exposition to category theory will be assumed.
Speaker Intro
Jürgen Fuchs is a professor of theoretical physics at Karlstad University, Sweden. He has obtained his PhD in 1985 at Heidelberg University, Germany. Jürgen's research interests are low-dimensional quantum field theories and the mathematical structures needed for their investigation. For a CV see https://jfuchs.hotell.kau.se/gen/cv_5.html.