Perturbative and Geometric Analysis of the Quartic Kontsevich Model
The analogue of Kontsevich's matrix Airy function, with the cubic potential Tr(Φ³) replaced by a quartic term Tr(Φ⁴) with the same covariance, provides a toy model for quantum field theory in which all correlation functions can be computed exactly and explicitly. In this paper, we show that dis...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211442 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Perturbative and Geometric Analysis of the Quartic Kontsevich Model. Johannes Branahl, Alexander Hock and Raimar Wulkenhaar. SIGMA 17 (2021), 085, 33 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | The analogue of Kontsevich's matrix Airy function, with the cubic potential Tr(Φ³) replaced by a quartic term Tr(Φ⁴) with the same covariance, provides a toy model for quantum field theory in which all correlation functions can be computed exactly and explicitly. In this paper, we show that distinguished polynomials of correlation functions, themselves given by quickly growing series of Feynman ribbon graphs, sum up to much simpler and highly structured expressions. These expressions are deeply connected with meromorphic forms conjectured to obey blobbed topological recursion. Moreover, we show how the exact solutions permit us to explore critical phenomena in the quartic Kontsevich model.
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| ISSN: | 1815-0659 |