2d Sinh-Gordon model on the infinite cylinder
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910048231358464 |
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| author | Guillarmou, Colin Gunaratnam, Trishen S. Vargas, Vincent |
| author_facet | Guillarmou, Colin Gunaratnam, Trishen S. Vargas, Vincent |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 2d Sinh-Gordon model on the infinite cylinder Guillarmou, Colin Gunaratnam, Trishen S. Vargas, Vincent Probability Mathematical Physics 60K35, 81T40 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. |
| title | 2d Sinh-Gordon model on the infinite cylinder |
| topic | Probability Mathematical Physics 60K35, 81T40 |
| url | https://arxiv.org/abs/2405.04076 |