Dual form of the paperclip model

The “paperclip model” is 2D model of quantum field theory with boundary interaction defined through a special constraint imposed on the boundary values of massless bosonic fields [S.L. Lukyanov, et al., hep-th/0312168]. Here we argue that this model admits equivalent “dual” description, where the boundary constraint is replaced by special interaction of the boundary values of the bosonic fields with an additional boundary degree of freedom. The dual form involves the topological θ-angle in explicit way.