λ-Deformations in the upper-half plane

Abstract

We formulate λ-deformed σ-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter λ and for large values of the level k of the underlying WZW model. To perform our computations we use either conformal perturbation theory in association with Cardy's doubling trick, as well as meromorphicity arguments and a non-perturbative symmetry in the parameter space (λ,k), or standard QFT techniques based on the free field expansion of the σ-model action, with the free fields obeying appropriate boundary conditions. Both methods have their own advantages yielding consistent and rich, compared to those in the absence of a boundary, complementary results. We pay particular attention, albeit not exclusively, to integrability preserving boundary conditions.