Bosonic Theory with a Random Defect Line

We study a two-dimensional bosonic field theory with a random defect line. The theory has a background field coupled to the field variables at the defect line, which renders the model non-integrable. However, as the background field is random, and the disorder is implemented through the replica trick, the model becomes integrable, allowing us to use the form-factor method to compute the exact correlation functions of the quenched model.