Theoretical Physics Seminar: Donald Youmans

  • Date: –15:00
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 Å80101
  • Lecturer: Donald Youmans
  • Contact person: Vladimir Procházka
  • Seminarium

Two-dimensional BF theory as a CFT

Two-dimensional abelian BF theory is an example of a topological gauge theory. Imposing the Lorenz gauge-fixing condition introduces an auxiliary geometric data 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). Going beyond Q-cohomology, i.e. studying correlation functions and OPEs of non Q-closed objects, allows one to define interesting structures such as topological correlation functions, a BV algebra structure on the Q-cohomology and an analog of Gromov-Witten invariants on the moduli space of punctured Riemann surfaces. 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.This is a joint work with Andrey Losev (University Higher School of Economics Moscow) and Pavel Mnev (University of Notre Dame).