Perturbation Theory for Conformal Field Theories
I will talk about perturbation theory for two dimensional conformal field theory (CFT). Just as in ordinary quantum field theory, it leads to a perturbation series, each term of which needs to be regularized. I will particularly focus on perturbations by exactly marginal operators, which lead to a moduli space of CFTs. There is a conjecture by Gukov and Vafa that rational CFTs are dense in some of those moduli spaces. This work is partly an attempt to investigate this conjecture.