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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2021 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2021
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211442 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| 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| _version_ | 1862642024063172608 |
|---|---|
| author | Branahl, Johannes Hock, Alexander Wulkenhaar, Raimar |
| author_facet | Branahl, Johannes Hock, Alexander Wulkenhaar, Raimar |
| citation_txt | Perturbative and Geometric Analysis of the Quartic Kontsevich Model. Johannes Branahl, Alexander Hock and Raimar Wulkenhaar. SIGMA 17 (2021), 085, 33 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-15T07:11:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211442 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T07:11:09Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Branahl, Johannes Hock, Alexander Wulkenhaar, Raimar 2026-01-02T08:34:55Z 2021 Perturbative and Geometric Analysis of the Quartic Kontsevich Model. Johannes Branahl, Alexander Hock and Raimar Wulkenhaar. SIGMA 17 (2021), 085, 33 pages 1815-0659 2020 Mathematics Subject Classification: 81T18; 81T16; 14H81; 32A20 arXiv:2012.02622 https://nasplib.isofts.kiev.ua/handle/123456789/211442 https://doi.org/10.3842/SIGMA.2021.085 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. It is a pleasure to dedicate this paper to Dirk Kreimer, who substantially supported this research project. The groundwork [31] was laid during the Les Houches 2018 summer school “Structures in local quantum field theories” organised by Spencer Bloch and Dirk Kreimer. AH and RW would like to thank Karen Yeats and Erik Panzer for the invitation to present our results at the IHES remote conference “Algebraic Structures in Perturbative Quantum Field Theory” in honour of Dirk Kreimer’s 60th birthday. Our work was supported⁸ by the Cluster of Excellence Mathematics M¨unster and the CRC 1442 Geometry: Deformations and Rigidity. AH is supported through the Walter Benjamin fellowship.⁹ en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Perturbative and Geometric Analysis of the Quartic Kontsevich Model Article published earlier |
| spellingShingle | Perturbative and Geometric Analysis of the Quartic Kontsevich Model Branahl, Johannes Hock, Alexander Wulkenhaar, Raimar |
| title | Perturbative and Geometric Analysis of the Quartic Kontsevich Model |
| title_full | Perturbative and Geometric Analysis of the Quartic Kontsevich Model |
| title_fullStr | Perturbative and Geometric Analysis of the Quartic Kontsevich Model |
| title_full_unstemmed | Perturbative and Geometric Analysis of the Quartic Kontsevich Model |
| title_short | Perturbative and Geometric Analysis of the Quartic Kontsevich Model |
| title_sort | perturbative and geometric analysis of the quartic kontsevich model |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211442 |
| work_keys_str_mv | AT branahljohannes perturbativeandgeometricanalysisofthequartickontsevichmodel AT hockalexander perturbativeandgeometricanalysisofthequartickontsevichmodel AT wulkenhaarraimar perturbativeandgeometricanalysisofthequartickontsevichmodel |