Seminarium KMMF "Teoria Dwoistości"

In Segal’s axiomatisation, a chiral conformal field theory (CFT) is a projective, monoidal functor from compact Riemann surfaces to the category of Hilbert spaces and Hilbert-Schmidt maps, satisfying natural compatibility conditions under gluing and boundary reparametrisations. The formalism is constructed to capture key properties of the path integral while avoiding measure-theoretic difficulties.Once a CFT is shown to satisfy Segal’s prescriptions, analytic control over central objects in alternative axiomatisation schemes (e.g. vertex operator algebras) is expected to follow. However, Segal CFTs are notoriously difficult to construct with concrete examples being few and far between. In this talk, I will review Segal’s framework and present a construction of the massless free boson CFT.