2d Sinh-Gordon model on the infinite cylinder
| Autor: | Guillarmou, Colin, Gunaratnam, Trishen S., Vargas, Vincent |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For $R>0$, we give a rigorous probabilistic construction on the cylinder $\mathbb{R} \times (\mathbb{R}/(2\pi R\mathbb{Z}))$ 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. Comment: 36 pages, typos corrected |
| Databáze: | arXiv |
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