Special Math/Physics Seminar

Vertex Operator Algebras and Conformal Field Theories

Christoph Keller

ETH, Zurich

Conformal Field Theories (CFT) are an important concept in physics. In two dimensions, there exists a mathematical rigorous description for them in terms of vertex operator algebras (VOA). In the first part of my talk, I will discuss some work on such VOAs, with a particular focus on VOAs with an infinite number of modules, which are not very well understood. I will also briefly discuss applications to Calabi-Yau geometry and to quantum gravity. In the second part of my talk, I will discuss ideas of how to generalize VOAs and other concepts from two to higher dimensions. I will namely discuss so-called Cauchy fields and the conformal bootstrap program.