二维双曲正弦-戈尔登模型在无限圆柱上的研究
2d Sinh-Gordon model on the infinite cylinder
AI总结：
本文研究了二维双曲正弦-戈尔登模型在无限圆柱上的概率构造，通过高斯自由场和量子算子谱分析，证明了模型的n点相关函数具有标度关系及离散谱特性。
摘要：
对于R>0，我们在圆柱体ℝ×(ℝ/(2πRℤ))上给出了一种严谨的概率构造，用于构建(无质量)双曲正弦-戈尔登模型。特别是，我们定义了该模型的n点相关函数，并展示了这些函数在R下表现出标度关系。该构造依赖于无质量高斯自由场，基于与该模型相关的量子算子的谱分析。利用高斯乘法混沌理论，我们证明了该算子具有离散谱和严格正的基态。
英文摘要：
For $R>0$, we give a rigorous probabilistic construction on the cylinder $\mathbb{R} \times (\mathbb{R}/(2πR\mathbb{Z}))$ of the (massless) Sinh-Gordon model. In particular we define the $n$-point correlation functions of the model and show that these exhibit a scaling relation with respect to $R$. The construction, which relies on the massless Gaussian Free Field, is based on the spectral analysis of a quantum operator associated to the model. Using the theory of Gaussian multiplicative chaos, we prove that this operator has discrete spectrum and a strictly positive ground state.
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