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 $(\lambda ,k)$, 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.

我们将上半平面的λ变形σ模型表示为QFT。对于不同的边界条件，我们精确地在变形参数λ中以及对于基础WZW模型的水平k的较大值，计算电流和主算符的相关函数。为了执行我们的计算，我们使用保形摄动理论结合Cardy的加倍技巧，以及亚纯性参数和参数空间中的非摄动对称性$（\lambda ，ķ）$，或基于σ-模型作用的自由场展开的标准QFT技术，其中自由场遵循适当的边界条件。与没有边界互补结果的方法相比，这两种方法都有其自身的优点，即产生一致且丰富的结果。尽管不是排他性的，但我们特别注意保留边界条件的可积性。