Donald Ray Youmans (Geneva): Two‐dimensional BF theory as a CFT

We present a construction of 2d TCFTs via gauge fixing topological gauge theories: Two‐dimensional abelian BF theory is an example of a topological gauge theory. Imposing the Lorenz gauge‐fixing condition introduces an auxiliary geometric datum in form of a metric. We will show that the theory becomes topological conformal, i.e. it depends only on the conformal structure of the introduced metric. Moreover, the stress‐energy tensor is Q‐exact (hence vanishes in Q‐cohomology and therefore on physical states). The Q‐primitive of the stress‐energy tensor can be used to deform the model. In particular, the non‐abelian theory can be seen as a deformation of the abelian one in the space of TCFTs. The former shares many features of a logarithmic CFT, such as the appearance of logarithmic singularities in OPEs. Notably, the presence of infinite Jordan cells of the Hamiltonian lead to vertex operators.