The singularities of Selberg- and Dotsenko-Fateev-like integrals
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917855988023296 |
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| author | Sussman, Ethan |
| author_facet | Sussman, Ethan |
| contents | We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ's minimal models of 2D CFT as described by Felder and Silvotti and Dotsenko and Fateev (the ``Coulomb gas formalism''). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call ``DF-symmetric,'' we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03750 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The singularities of Selberg- and Dotsenko-Fateev-like integrals Sussman, Ethan Mathematical Physics Classical Analysis and ODEs Primary 32A20, Secondary 33C60, 33C90, 81T40 We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ's minimal models of 2D CFT as described by Felder and Silvotti and Dotsenko and Fateev (the ``Coulomb gas formalism''). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call ``DF-symmetric,'' we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods. |
| title | The singularities of Selberg- and Dotsenko-Fateev-like integrals |
| topic | Mathematical Physics Classical Analysis and ODEs Primary 32A20, Secondary 33C60, 33C90, 81T40 |
| url | https://arxiv.org/abs/2301.03750 |