Free-field realisation of boundary states and boundary correlation functions of minimal models

TL;DR

This paper develops a formalism using free-field methods and Coulomb-gas techniques to compute exact boundary correlation functions in minimal models, exemplified by the critical Ising model.

Contribution

It introduces a new algebraic approach to connect boundary states with correlation functions, enabling exact calculations in boundary conformal field theories.

Findings

Reproduces known results for the critical Ising model

Provides a systematic method for boundary correlation functions

Links boundary states with observable correlation functions

Abstract

We propose a general formalism to compute exact correlation functions for Cardy's boundary states. Using the free-field construction of boundary states and applying the Coulomb-gas technique, it is shown that charge-neutrality conditions pick up particular linear combinations of conformal blocks. As an example we study the critical Ising model with free and fixed boundary conditions, and demonstrate that conventional results are reproduced. This formalism thus directly associates algebraically constructed boundary states with correlation functions which are in principle observable or numerically calculable.