Coulomb-gas approach for boundary conformal field theory

Abstract

We present a construction of boundary states based on the Coulomb-gas formalism of Dotsenko and Fateev. It is shown that Neumann-like coherent states on the charged bosonic Fock space provide a set of boundary states with consistent modular properties. Such coherent states are characterised by the boundary charges, which are related to the number of bulk screening operators through the charge neutrality condition. We illustrate this using the Ising model as an example, and show that all of its known consistent boundary states are reproduced in our formalism. This method applies to $c<1$ minimal conformal theories and provides an unified computational tool for studying boundary states of such theories.