Coulomb-gas approach for boundary conformal field theory

TL;DR

This paper introduces a Coulomb-gas formalism-based method for constructing boundary states in boundary conformal field theories, demonstrating its effectiveness with the Ising model and applicability to minimal models with central charge less than one.

Contribution

It develops a unified Coulomb-gas approach for boundary state construction in minimal conformal theories, reproducing known states and enabling systematic analysis.

Findings

Successfully reproduces all known boundary states of the Ising model.

Provides a consistent framework with modular properties for boundary states.

Applicable to all $c<1$ minimal conformal theories.

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.