HEP Theory Journal Club

The Virasoro fusion kernel and its applications

Yan Gobeil

McGill

Analytic tools for the conformal bootstrap in d>2 dimensions have grown very useful in the past years and I will review a few of them. Most of these tools have yet to be used to study 2d CFTs, especially at finite central charge. I will present an object known as the fusion kernel that was derived from the representation theory of the Virasoro algebra some time ago by Ponsot and Teschner but has not been used that much to study CFTs. Crossing symmetry can be rewritten using this fusion kernel and I will show how to use it to find results about the spectrum of operatos in 2d CFTs at finite c. These results will be used in the large spin expansion and will help us study the late time behavior of Virasoro blocks.